The Rocket & String Paradox
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- Опубліковано 17 сер 2021
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This video is about Bell's Spaceship Paradox of Special Relativity, wherein a pair of rockets (or spacecraft) connected by a weak thread accelerate with uniform acceleration, maintaining the same separation, and the question is: does the thread break? And if so, why?
REFERENCES
Interactive Spacetime Globe by Alexander Wu:
alexonscience.com/projects/sp...
Read an overview on Wikipedia:
en.wikipedia.org/wiki/Bell%27...
John Baez on Bell's Spaceship Paradox, Rindler Acceleration, etc
math.ucr.edu/home/baez/physic...
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Relativity is one of those things that just makes things weirder the more you explore its implications.
If you explore it enough it all starts to make sense again.
It’s like a really complex set of rules that results in a perfectly balanced game.
Right? Like there’s two ways to understand the situation and they both lead to the same result. Time dilation making muons decay slower from earth’s perspective, and length contraction making the earth thinner so the muon can travel farther before it decays, from the muon’s perspective
I had an idea based if E=mc^2
Dose that mean hotter things are heavier
Maybe because people assume explanation is absolute. But it is relativity itself which is explained.
Einstein boards a train and asks, "Does Boston stop at this train?"
Good one haha
hehe
The conductor says "yes, but not yet. Stay on the train, and Boston shall come to you."
Boston does not experience acceleration towards the train. The train experiences acceleration towards Boston...
"ah, you must be a foreign language speaker. yes, Boston is visited by this train. you mistaked 'visit' as 'stop at"
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.
which is what he stated originally. that they started at the same time. so he contradicted himself to mislead or whatever
@@aliceslab If the rockets started at the same time from their own perspective (or rather, from the perspective of the front rocket), then a stationary observer off to the side wouldn't see them both start at the same time. A 'true' observer, so to speak, would observe the back rocket starting first.
@@equidistanthoneyjoy7600i was never given a value to the distance between. so things arent being presented clearly
@@aliceslab The length of the rope isn't important, it's under the same forces either way.
@@equidistanthoneyjoy7600 it is important. if the rockets were close enough in the same area the time would actually be the exact same that they start. time differential and special relativity is only valid if you have a certain distance among each object.
so the only reason the string breaks is because the rockets were far enough away that the time was changed due to special relativity
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 :)
Are you serious? I only had basic coverage of relativity in high school and found there was nothing surprising here, I anticipated the whole video just from the setup of the problem. Situations like this with a duality of the explanation for one reference frame or another are basically the whole theme of relativity. For instance, one example I remember that they gave me in high school, was a 10 meter pole passing through a 5 meter long barn at 90% the speed of light. From the barn's reference frame, the pole is contracted to a length of 10*sqrt(.19) or 4.36 meters so it can fit entirely within the barn, and both the front and back barn doors can be briefly closed with the pole completely contained within it. But from the pole's reference frame, it is the barn that is contracted, to 2.18 meters in length, so how can the 10 meter pole fit within the 2.18 meter barn? The answer is, because from the pole's reference frame, the front and back doors of the barn aren't shut at the same time. It is all because there is no universally defined simultanaeity, the barn thinks the doors were shut simultaneously, the pole does not think those 2 events happened at the same time.
The one thing he should have mentioned is that eventually, an event horizon actually appears between the 2 ships and it becomes impossible for the ship behind to send a message that is ever received by the one in front because the light they send never catches up to it, but the one in front can still always send a message to the one behind, provided they continue constant acceleration forever.
They had to put the energy into the string to keep up with the two rockets. The rear rocket is a pushing force, which is to say it wouldn't accelerate the string which relies on tension.
The forward rocket will however pull it forward. At a given energy level the force needed to get to a higher speed is higher because the energy required to reach that speed is higher. So arguably for any string of any length or any strength we should be able to calculate how fast you need to be going to reach its Yield strength as a function of the speed of light, based on the instantaneous acceleration.
So no matter how fast or slow you choose to accelerate forever you will snap off the connection point of the forward spacecraft regardless of the force being measured as an increase of tension, the energy required to accelerate that string, or the spacecraft being drawn together.
I'm just unsure if the string would also fail at it's pushing end at the same time, as arguably the forces at both ends should be equal as from the strings perspective it is being acted on at both ends and remaining stationary in the middle 🤔
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!
I see what you did there ^^
Clickbait ;)
I wish there was a good video about how thumbnails and titles should be designed for youtube videos. Bonus points if the host presents everything standing on a ladder!
Be careful. Ask yourself the opposite: what if it wasn't a string, but a strut, or one ship and two engines? What's the difference? Combine the engines and you'll see that the only difference is the speed of sound in the material chosen, and then that necessarily any material will get torn apart at some factor of length contraction.
I get what you did there ;)
You’re tearing me apart, Einstein!
Oh Hi Neel
You're my favorite Neel.
ha ha ha what a story Mark
@@PublicVoidFoo neel* 😂
Soooo. Football then.
Engineer: *Any real string would break from accelerating its own mass before relativistic effects are important*
Actually no, you can make the acceleration quite slow and eventually the string would be stretched beyond it's breaking point and snap due to relativistic effects (the ships have to resist yielding to the string tension tho).
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
Title and thumbnail sounds like minutephysics watched Veritasium's video on Clickbaiting. "Do Salt Lamps Work?" "No." 😂
Exactly! 😂
Seems like your switched on today
But it's different. It says "Yes."
Tought the same.
Also Verisatium made a video yesterday about clickbait talking about this: "Clickbait is Unreasonably Effective". Really cool video.
@@sacktar that’s the video op is talking about
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.
The string is an accelerating reference frame, not an inertial frame, so you can't apply the static -time dilation- length contraction math to it (this is why the video mentions a frame moving at the rocket/string system's *final* speed)
I feel like this video suffers from the same issues most 'look, relativity paradox'-videos suffer from: they describe a situation using a general time and distance.
"Both craft suddenly accelerate the same amount at the same time"
Both "accelerate the same amount" and "at the same time" in that statement mean different things from different perspectives, and thus the question is ambiguous. It is an equally valid interpretation that they accelerate the same amount at the same time, as viewed from the space craft. Then, still viewing from the space craft, there is no relative motion, no length contraction, and the string stays intact.
I'd have to calculate how this would look from an outside observer, but probably something along the lines of: the space craft don't accelerate the same amount at the same time, but the length contraction counteracts this to keep the string taut.
The trick is to understand that the two spaceships are equally apart at the point in time in which they start accelerating, as when they were stationary! There is no length contraction in the space between them! But the rope, since it is a body held by the binding forces of its atoms, experiences length contraction. Therefore that rope becomes shorter, but the distance between the spaceship doesn’t, and this leads to higher tension on the rope. The electromagnetic fields which hold the rope together change when the rope starts accelerating, that’s where the forces which keeps it together change. Now take a rope which is weak enough to brake at the slightest added tension, and that rope will definitely break.
See again the reativity simultaneity
@@_Xeto The trick is in realizing that this video interprets its own setup in one way, while a different way is equally valid.
The video states that for the POV of the space craft, simultaneous events no longer are simultaneous. But this is in direct contradiction to the setup of the paradox, which states that they do start at the same time.
The trick is that the video doesn't mean they 'start at the same time'. It means to say they 'start at the same time as viewed from an outside observer.' Change that to 'start at the same time as viewed from the space craft' and the argument falls apart.
"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.
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
That was my thought too, where does the ship not be a ship. How many rockets do you need?
@@xenorac - when is a frame not a frame but 2 frames - just because of where 2 objects start out. Rediculous. Bell's analysis contradicts SR. Two objects start at same time in same frame - either they length contract towards each other or length contraction is itself a contradiction of SR. SR is a total mess of logical [illogical] contradictions, But people take it seriously. seriously
except the set up stipulates that the rockets always appear equally separated from an outside perspective.
@@DrDeuteron Actually it doesn't. And if you do that, one of the rockets will have to eventually exceed light speed according to the ground observer. Common sense therefore says it makes sense to assume each rckt feels the same acceleration.
Also, Bell was actually stating that SR is impossible - because he says any gaps between objects cannot suffer length contraction. He's contradicting himself on numerous levels
@@jeromehattkronen2305 that's not how relativity works. Just do the Lorentz transformation and show me where you are right. If you haven't done the math, then fuggetaboutit.
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?
Well yeah because you would create slack in the rope
The term "sooner" loses its meaning as the rockets accelerate.
@@KerbalFacile not really
Then you would just make the sting less stressed, and the problem is thus rendered irrelevant, so it's only a solution from a certain point of view.
It depends. If the time between the two ignitions is large enough, the back rocket will pass the front rocket, and fly ahead, and the rope will snap because it gets too far ahead and is faster. No relativity needed.
If the front rocket engine ignites soon enough after the back rocket, then it will manage to stay ahead, and eventually the rope will again tighten up the slack, and then snap.
There is a sweet spot in-between where the back rocket will keep closing in on the front rocket indefinitely (even from its own reference frame), but never catch up to it.
Taking a page out of Veritasium's book for the title. I like it!
I was going to say the same
Even the thumbnail is the same
Yes.
Ayy! I came directly from veritasium's video on type 1 clickbait!
I was thinking the same thing!
Me too
I've seen this video everyday since it was released and I learn something new each time.
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.
ufff thank You for that. I was thinking I'm only one seeing this this way.
I think in order for the acceleration to be "simultaneous" in the perspective of the front rocket, the rocket on the back need to accelerate earlier than the front rocket
allowing stretching completely invalidates the thought experiment. But if you did, it would not look longer, it would be longer.
@@DrDeuteron When he says stetched here he means stretched taut, meaning that the string did not become loose, but maintained it's length the entire time.
@@JohnSmith-vq7gg you're right, but OP is still messed up. There is only one frame in which ships have constant separation, and the string breaks in it because each ship sees the other moving away, in all other frames.
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.
HOT DOGS, HOT DOGS, GETCHA HOT DOGS, FIVE DOLLARS!!!
@@MildSatire are you the gatekeeper lmao
@@xynyde0 Lol. Fanboys are strange creatures.
@@JamesBiggarHOT DOGS! FIVE DOLLARS!
Why do you need to ”save the data” ?
"Can Length Contraction Tear You Apart?" thumbnail: "yes"
alright then, i guess i don't need to see the video, i have the answer
But do you know WHY it can tear you apart? Thought so.
@@AlexanderMichelson yes
@@sandifirmansyah1988 why?
i think this is a spin off of veritasiums latest video
Because it's "length ( space between two objects)" not "object inside space"
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.
No, it cannot. If the ends of a rod accelerate equally as stated, the rod breaks. See: Born Rigidity.
Holy shit you guys are bad at thought experiments @@DrDeuteron
@@Blazingbiskit why? This thought experiment isn’t about properties of materials. The point of the string is that it isn’t strong, so you don’t focus on strength, but ppl always do. If you were to do that, though, you could restate the problems as: if you had a really strong rod and stretch it by an unbound factor, does it break?
@@DrDeuteron Incorrect. From an engineering standpoint, any real rod not only has a strength, but it can also stretch to some extent, which is why engineers care about the modulus of elasticity of materials. Born rigidity is a theoretical concept just as classical rigidity is; it's not applicable to real world problems any more than spherical cows are.
@@psychohist engineer = stay in the 📦
Physicist….what 📦?
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.
I found the opposite - that the video was extremely confusing on first viewing. It was only after working out the problem separately that I deduced what actually happened. Then on second watching the video made sense. So basically, the video makes sense if you already know the answer, which makes it nonexplanatory. But he got two views from me, so that's a win for him - if he'd provided a video that actually explained what was going on, he'd onlyl have gotten one view.
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".
Exactly at that timestamp you have the answer. Events that happen at the same time no longer appears to do so because of relativistic effects.
@@ToroidalX I know, that's the explanation that needs further detailing. Just mentioning this mind-boggling effect that speed has on "reality" It's not something that average viewer is able to hear and just continue with the video like "oh, yeah, that's right, that does happens...". It's so out of the ordinary that it even contradicts the "at the same time" that was one of the only 2 premisses at the beginning of the video.
@@inlegivel at relativistic speeds nothing is intuitive. The video talks about a though experiment. If you need more info about relativistic effects you can search more detailed videos! After all, is minute physics haha. He always makes short videos and assumes the viewers have some knowledge prior
@@inlegivel No it's not that it's hard to understand, it is just wrong. If 2 objects independent or semi independent like 2 rockets with rope attached to them, if they accelerate at the same time, at the same rate, time dilates to both of the the same way. If it was a graph, with the time dilation of both objects acceleration at a constant identical rate, it would look like a linear function, with both lines overlapping. Saying that the first rocket somehow get's time dilated first, is just... weird, since we KNOW that they start at the same time with the same dilation
@@HaartieeTRUE No one is saying any of what you're claiming they are. You need to look into this, that's the only solution here.
All I can say is time dilation and the relativity of simultaneity are two different things.
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!
This is a pointless though exercise
It deals with absolutely NO REAL PROBLEM
IT won't be reached by any technological way in a near future
And all said here is THEORETICAL nobody can even test the teory
So your "IMAGINATION AND CREATIVITY" is much like a person high on weed laughing at nothing and saying bullcrap
POINTLESS
@@rafaellima381 is nihilism hitting you hard, friend? Watch Optimist Nihilism, a wonderful video from Kurzgesagt
@@DefnitelyNotFred não assisto esse canal É scifi para crianças...
Minute physics, muitos videos coerentes e informativos
Kurzgesagt é só bobagens de vídeo games, filmes e teorias malucas que crianças e adolescentes gostam de ver
@@rafaellima381 Science deals with knowing the unknown. Engineering is the field of applying the science to real problems. Science is not concerned with what that knowledge can or cannot be used for
@@rafaellima381 , *_"And all said here is THEORETICAL nobody can even test the theory"_* - What makes you say that? It's completely testable with today's technology.
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
Finally a new video! Where have you been, glad you're back :)
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!
Premieres don’t build up excitement, they build up irritation.
@@ChazM003 the cool part is that you can look back at people's reactions
@@ChazM003 I watch a lot of channels who do weekly premieres, all of them have the usual 99% like/dislike ratio. What this comment section proves is that a small amount of negative reactions will seed bigger negative reactions.
@@GuyWithAnAmazingHat The video is great as usual, I’ve watched this channel for a long time. I personally don’t like the Premier feature, and I am apparently not alone. There’s a difference between negativity and constructive criticism.
@GuyWithAnAmazingHat I love this channel, and I didn't dislike the video because it used the premiere feature.
Maybe this audience here is more averse to mechanisms that exploit human curiosity to get people to think of UA-cam more (because they know that this video will come out, but could not watch it yet), and ultimately lead to more screen time.
Anyway, I would love if the premiere feature got removed eventually because it was too unpopular among viewers.
Feels kinda weird having a premiere for what i assume is a 5-10min video
Your assumption was wrong, it was a 3 minute video!
Can I ask what happened? I am confused
@@thehiddenninja3428 just that it was a premiere for 5h before it went live, and a lot of people didn't like that
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 !
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.
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
use the set a reminder button
@@ELYESSS nobody uses it, because nobody uses notifications. people who do, are weirdos
normal people just go to the subscriptions to see what's uploaded.
I concur, it’s a letdown at the time when you find something interesting and realize you can’t watch it. UA-cam doesn’t provide users the option to not see “premiers” that are still pending, so the only way for users to avoid it is to unsubscribe channels that use it.
@@ELYESSS Why should I? This is video on demand, it exists because scheduled TV is stupid. I want to watch videos when I feel like it. I will not arrange my schedule around a video being freshly available.
@@PsyKeks am pretty sure you can use adblock filters to block premiere videos if it is bothering you guys too much
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.
Just as the ladder cannot fit entirely inside the barn from one viewpoint but crash through the barn door from another viewpoint.
You don't need GR to know that much - in fact, you don't even need _SR_ ; all you need is general covariance, which is a thing even in Newtonian mechanics...
@@whitslack That’s actually explained in a similar way as the rockets here…
Dr Don has a great explanation for that on Fermilab channel.
A good example is for example a mistake in a scientific article I read somewhere, where they said that relativistic speed raises the mass of the rocket, and it will turn into a black hole. That’s not true, and cannot be explained away.
@@juzoli , that's a misinterpretation by whoever wrote that article as to what is meant by "relativistic mass", and how it is not actually mass, but in a sense it _is_ inertia.
@@JivanPal Yes, and the fact that you cannot possibly reconcile the 2 viewpoints, shows that it cannot work like that.
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
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.)
Your conclusion is correct, this video is fundamentally wrong. The entire reference frame of two spaceships maintaining stationary positions of zero relative motion together, would experience length contraction in its entirety. The ships, the rope, the people on it, would not notice anything except the feeling of acceleration.
@@JeffreyBoser i said this to some other guy too:
Most of these people don't understand that whatever other point of reference they get is irelevant, because the 2 ships are stationary to each other.
I don't think the video disagrees with you. The ships do experience this tidal force and the materials adjust their shapes accordingly.
The string is prevented from shortening by the ships which aren't getting closer to each other.
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.
...I uhh still don't get it, why does the front one accelerate faster?
@@enderallygolem Relativistic effects at speeds near light speed i guess
im glad we dont need to watch the video anymore. Thanks!=)
@@enderallygolem There is no such thing as the same acceleration for objects behind or in front of you. Only objects that move exactly parallel to you can have the same acceleration. It is weird as hell.
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'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.
Main reason I downvote this every time I see it, I use an external RSS feed to ensure I see all videos from a creator. This breaks that use case. For people who badger their audience to subscribe, ring the bell, like, kill a chicken in an offering to the subscription button gods you'd think they wouldn't mess with the one method that guarantees their subscribers see each and every video.
"...begin feeling negatively about a video that they've yet to even watch"
what do you mean?
you would think the answer is no but the thumbnail says "yes". So I'm very eager to learn why
That sounds like a you problem
@@greyed youtube really doesn't like outside rss users.
(I am one of them)
Because the ads will not play.
I use NewPipe, and i sorta don't like it.. because I can't have an account and press like on videos easily
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?
i don't think you are wrong. i also thought this and also what about cutting the string near the back rocket. how does the string and the back rocket interact? i only see them moving uniformly.
I agree, the illustrations don't include this. *Spacetime itself* undergoes length contraction, so the distance between the rockets also contracts, which the illustrations don't show. Now, there might still be some temporary tension induced in the string while the acceleration occurs, due to the relativity of simultaneity issue, but I strongly disagree with Henry's more general explanation and illustrations on this one.
@@ninjafruitchilled I think that if you include the fact that the string is a physical object itself, which is pulled from the front (the rope is explicitly not instantaneously accelerated along with the rockets, it's merely connected to them), just the acceleration of the front rocket would apply a tension force to the string and that force won't propagate along it instantaneously, or even at lightspeed, but in fact it would travel only at the speed of sound in that material (which is slower, and I believe it must be slower by definition, and that means that the tension would form a gradient along the length of the rope, rather than being static like in a steady-state system). So I think that the rope's own inertia is what actually snaps it, in the initial 'stationary' reference frame. This seems like the obvious answer to me, unless there's some reason to ignore the effect (which I don't think there is, after all the rope is said not to be strong enough to pull the second rocket).
@@killerbee.13 Yeah I agree, the rope doesn't even "know" about the existence of the back rocket for quite some time (relatively speaking ;)), so if your criteria for snapping is simply that tension is induced in the rope then yes it snaps even if it isn't tied on to anything.
@@ninjafruitchilled Exactly, I thought of the same thing. It just doesn't add up
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
So when my mum said "you're tearing this family apart" she really meant "length contraction causes this family to accelerate at different times!"?
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 😂
does anybody know how to turn off notifications on premiers in the sub feed?
Minutephysics answering questions we didn't know we had and would have wanted answered
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.
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?)
where did you get the idea that the spaceship on the back would accelerate first in its perspective? Also, both ships accelerate together from an outside perspective. On the perspective of the rockets after they have accelerated the one on the front accelerated first, so the strig snaps.
@@enderyu THERE IS LITERALLY NO REASON THE FRONT ONE WOULD ACCELERATE FIRST.
relative to the earth they fire simultaniously, and relative to each other they also fire simultaniously. They have the same vector of movment, so they are not dilated in space time to each other. The only case where "things that appear from a perspective to be simultanious no longer are from another" like he said in the video only works for things which have different time dilations from the start. ex. object a is stationary compare to earth, object b is moving 1/2 speed of light compare to earth. thus time is 50% slower. both objects blink a light at the same time. In this case one of the 2 actually blinks it first (no idea which tho).
@@enderyu To more simply ilustrate how dumb the idea that the first rocket magically fires first if observed from somebody else is:
A) 2 rockets one next to each other instead of one behind them. (put a rope in between them if you think the argument is not equievalent) does one suddenly fire first or something ? NO of course not. why does puting it behind make it fire later but putting it on the side not ? it doesn't. the whole point was that they have the same speed and direction relative to each other aka, from their pserspective, time is the same
B) One LONG rocket, with engines both in back and in the front. Does time dilation somehow magically appear and make the engine in the front fire first ?
@@HaartieeTRUE That is relativity for you. The rocket on the front is indeed going to fire first and not due to 'differences in time dilation'; If you look up Lorentz transformations you will see a term proportional to the position along the direction of motion of the frame you want to transform into (which will often be denoted by gamma*v*x/c^2, being x the direction of motion).
Therefore if both rockets are side by side they will fire simultaneously on both frames of reference, but with one in front and another behind they can only be simultaneous on one of the frames of reference (in this case, the rockets initial frame of reference [before the acceleration]).
Here are some references:
ua-cam.com/video/Rh0pYtQG5wI/v-deo.html
ua-cam.com/video/SrNVsfkGW-0/v-deo.html
You might have already seen these videos before (since its from this channel), but i think you were mixing up the scaling gamma factor (responsible for time dilation) with the other "shifting" term (responsible for desynchronization)
@@enderyu but it makes absolutely no sense, that from the perspective of the back-ship, the front-ship seems to accelerate first, when they actually accelerate at the same time. If that was the case, then you would fucking have time travel dude haha
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.
I agree. But how about LA CASA DE PAPEL 5th season on September 3rd? World's gonna stop.
@@misophoniq dafuq dude, if not sponsors they wouldn’t earn sheet, plus you can just use vanced…
@@misophoniq Don't just dislike videos with sponsorship ads in them. (unless they're in the middle of the video 😡) They came about for a good reason. I don't really understand the whole story, but it has to do with the "Ad-pocalypse" from a couple years ago. Watch a video from 2018-2019, and there's a 50/50 chance that there's a demonetization joke or a yellow circle with the dollar sign somewhere in the video - content creators suddenly lost reliable income from UA-cam, so they turned to Patreon and sponsors.
If you don't want ads on UA-cam, get a good adblocker or two. And then drop the Premium subscription - donate that money directly with Patreon, which many UA-camrs have. And if you like, send them a message asking them to drop the sponsorships. They'll take their patrons seriously.
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.
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.
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?
I'd guess there is always some amount of stress, that the material has to endure and building in a way that induces more stress, requires more stability, too. So there would be no "point at wich", other than the point where it was not built strong enough. But yeah, not at speeds and accelerations we are currently actually planning on using. 😄 Probably inertia will always be the bigger factor by far.
Oh and you talk about "thrust surface", so you mean next to each other? That would always stay next to each other, when flying straight. Only behind each other should make a difference. And by the time it becomes relevant to us, we can use computers to mudulate thrust to compensate. 😁 (And maybe have space-time stabilizers and be flying in warp bubbles anyway 😏)
I think all of those variables listed would have an effect, although I think the biggest one is the amount of acceleration that the engines produce. If its a smaller amount of thrust, then the amount of length contraction that is caused is small and therefore easily counteracted by electromagnetic forces.
@@PsyKeks I don't have a practical real world example, but this is a completely hypothetical issue anyway. My "thrust surface" idea was to challenge the boundary of what is considered separate engines. What if you had a continuous surface that could generate thrust, that could be spread from the front to the back of the craft? Not necessarily of a consistent width, cross section, or shape. Potentially even along the length of a small structural member, the size of a piece of string. Though I now realize an issue could arise in any slight variation in thrust. If the leading engine was the greater thrust/acceleration, then if the string were strong in tensile, then it might act as "one ship" and transfer the force through the structure as suggested in the video. If the leading were less, the following would eventually over take and become the leader.
To be honest, I think this problem is purely academic and pondering the consequences is thus inconsequential. I just thought there were some logical inconsistencies in the absolute presentation of the system as "this would definitely happen" and the infinite continuum of scenarios that exist between what wouldn't have this issue, and what would.
As you eluded to, We've unlikely to ever build a craft vast enough, that can go fast enough, for this to ever be a problem humanity has to solve.
I have a hard time buying this one, because 1) it's 7am and I just woke up 2) is there there really anything fundamentally different from multiple rockets firing versus one big cat accelerating? I mean sure there's a time factor that you need to take into place, but if you had a clock in the middle of the string telling them when to start accelerating they should accelerate simultaneously as the signal gets to them at the same time. and 3) From the perspective of the rockets they're not moving, however space around them is contracting so shouldn't the rockets appear to get closer?
It’s only in the initial (“stationary”) reference frame that the clock successfully synchronizes the rocket ignitions. In the fast-moving frame, which the rockets eventually inhabit, the closer rocket - the one that is ‘ahead of’ the other one - started first, which is why the string breaks.
@@notme98 Nope; the string doesn't break because one rocket revved up its engine first - it breaks because between inertial frames, the rockets have to accelerate - and it's _that_ acceleration that pulls the thread taut, as it's the only physical thing distinguishing between the otherwise equivalence of frames 1 and 2
@@thstroyur ...and the acceleration only pulls the thread taut because the front rocket started first. Because that implies that the speeds of the two rockets are diverging, and therefore the distance between them is (parabolically) diverging. If the speed of light were infinite, and special relativity did not exist, the acceleration would fail to cause the string to break, since the rockets would be able to start simultaneously.
@@notme98 "and the acceleration only pulls the thread taut because the front rocket started first" You're misunderstanding the meaning of simultaneity here; saying that "the front rocket started first" is a frame-dependent statement, and isn't even a kinematic requirement - you could just as easily program both rockets to accelerate so that, _as seen from the initial frame_ , they always have the same velocity - in which case the thread wouldn't even get taut. This can simply be seen by writing down parametrized expressions for the position 4-vector of each rocket: e.g., a rocket _instantaneously_ going from rest at the origin to cruise v at t=0 along the x-axis can be written, shortly, as *q* (t) = (q^0=ct, q^1=T(0)vt, q^2=0, q^3=0), where T(0) is Heaviside's step function. You can put another rocket initially displaced a x_0 from the origin, and play around with different acceleration regimes to see that, for some of these, the distance between the two rockets will get larger than x_0 as seen from the initial frame, but for others it won't. _All in one frame, bud_
@@thstroyur What do you mean with inertial frames...? I think I got everything in the video, expect for this one rocket accelerating first part.
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
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.
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?
As was mentioned, the "events" of each rocket starting to move don't happen simultaneously in the frame of reference of the rockets. In detail, on either rocket, you would observe that the front rocket moves first, stretching the string and snapping it.
@@tomfeng5645 That was never mentioned.
The frame in the video moves at the final speed of the rockets, not with the rockets.
From the back rocket's perspective, both rockets do indeed start accelerating simultaneously.
However, accelerating reference frames are weird. Time actually contracts in front of the rocket and dilates behind it due to this acceleration, so the rocket in front appears to start accelerating faster in this reference frame, pulling the string taught and snapping it.
@@alansmithee419 The video uses an idealized setup where the velocity change is instantaneous, with no period of acceleration
With light travel delay, in such a case, it would indeed look like the front rocket moves first.
Or, it would look like such as long as the acceleration period is shorter than the light travel time between the rockets, as the dilation happens while the opposite rocket appears stationary
You do raise a good point about how it would look should that not be the case
I think this question is relevant to determine the electromagnetic forces that affect the string's length in the starting frame and I thought time for light to roundtrip was the relevant quantity here.
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?
If there's a force pulling the rear ship forward there must being an equal an opposite force pulling the forward ship rearwards, conserving the linear momentum (not adding any energy/velocity to the system).
Otherwise you'd have an infinite acceleration device that lets you break the speed of light, go backwards in time, escape blackhole event horizons, etc.
@@isaiahphillip4112 "escape black hole event horizons."
Actually, no. It's not that light isn't fast enough to escape black holes, it's that there simply aren't any paths which exit the black hole from inside it. If you go faster than light, you'll simply spiral into the black hole faster. Space completely folds in on itself inside a black hole.
No it wouldn't and I have no idea why you think it would. If the rope was elastic it might briefly do that because of the stored energy but like that's just how slingshots work. It had nothing to do with relativity.
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.
Note, your sponsor Brilliant is impossible to unsubscribe from. I had to have my bank step in. Yes I followed all the rules!
You're tearing this family apart! With your simultaneous, but individual acceleration!
Lisa!
This thumbnail gives me salt lamp vibes
TECHNOBLADE NEVER DIES
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?
A tube of cold helium gas in the lab is full of perfectly spherical atoms (and nuclei).
If it the tube is moving, the atoms are oblate spheroids. mass is irrelevant.
"At the same time" "Aight Imma stop you right there"
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.
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 😬
There's a hidden subtlety, you can't treat accelerating reference frames as though they're inertial. The two frames Henry presented are inertial frames, but the frame with the rocket is non-inertial, so isn't equivalent to the other two frames.
The rope snaps during the acceleration, not when all frames are inertial
@@tommc1425 great clarification, thank you
You are mixing up the rocket's perspective with an outside perspective. If the rockets accelerate at the same time and by the same amount, then on that particular perspective their distances are going to be constant. You don't get shorter on your own frame of reference; similarly, the string is only going to get shorter if it doesn't accelerate with the rockets.
To summarize:
If the rockets accelerate at the same time and by the same amount on the *rockets* point of view:
Rocket POV: String's length is constant and so is the distance between the rockets -> Rope does not snap.
Outside POV: String is length contracted, but the back engine fires first decreasing their distance > Rope does not snap
If the rockets accelerate at the same time and by the same amount for an *outside observer* (situation shown in the video):
Rocket POV: String length is constant but the front rocket fires first, increasing distance between them -> Rope snaps
Outside POV: String length contracted but rocket's distances do not change -> Rope snaps
@@enderyu Thank you, I was thinking I am going insane, the issue in the video is that the way the reference frame is constructed thus insuring the rope will break.
@@enderyu ok, no THERE IS LITERALLY NO REASON FOR THE FIRST ROCKET TO FIRE FIRST. Same acceleration means same time dilation.
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!
Well that's not quite what happened. Einstein built heavily on works of people before him. Mainly Maxwell and Lorentz. I believe Length contractrion was originally Lorentz attempt to save the aether theory. But Einstein bit the bullet and declared the speed of light a law of nature and regorously described the consequences.
He deserves a lot of credit, but he didn't do it alone.
@@narfwhals7843 that's correct. It's supposed to mean "most" not "all". No single person can come up with such a complex theory from scratch all by himself.
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.
it is. In the P/B, the door separation remains fixed in the "rest" frame, and the pole contracts in that frame. IN this, the pole length remains fixed in the rest frame, and is torn apart in its own (average) rest frame...I say average, because the two spaceships have different rest frames, which is why they see each other moving away thereby breaking the string.
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.
Are you trying to say the string doesn't break? Yet from the proper reference frame you can observe the front rocket fire its engine first and therefore break the string.
@@jetison333 what makes a reference frame "proper" from another?
@@FickleWid by "proper" I just meant a specific reference frame that you choose.
@@jetison333 I understand what you mean. Say the observer is standing at the destination of the rockets, so he sees the rockets coming at him. The light from the front rockets arrives to him a few millisecond sooner and sees the front rocket accelerate first and get ahead while the rocket at the back stays still. The rope would appear to lengthen starting at the front and propagating backwards.
Another observer staging behind the rockets would see the opposite... The back rocket stays first, a few millisecond later the front rocket stays moving, while the rope appears to contract black to front.
Both of these views are subjective and caused by the light arriving at different times. Before the discovery of speed of light and Einstein's special theory of relativity, scientists couldn't reconcile this and that was the time the term length contraction was coined (from observing Jupiter's moons being ahead or behind of schedule on their orbits depending on where the planets where on their orbits)
To imagine this better, an observer staging far away somewhere perpendicular the startind position of the rockets would see both rockets and the rope accelerate together and no contacting or lengthening would happen according to him, because the light from both rockets and rope arrived to him at the same time.
Length contraction is not real, it's only perceived and caused by light from different parts of a fast object arriving art different times.
It's truly humbling what the nature comes up with to confuse and amuse us, when we look closer at things which aren't part of you ordinary experience!
@@_general_error Length contraction is definitely real, and has nothing to do with how the light hits your eyes. For example, lets say there's a star 1 light year away. If there was no length contraction, then from the perspective of someone going at a high fraction of the speed of light, they could not get there in under 1 year. However, that person sees that the universe is length contracted and therefore the distance to the planet is much less than 1 light year and so they can arrive at it in under a year from their perspective.
Same as for when the rockets fire. In general relativity, when your moving at a different speed than someone else, things that happen at the same time for them happen at different times for you, even when you account for how fast light travels. Under a certain reference frame, you see that one rocket fires first (accounting for the speed of light) before the other one does. Therefore the distance between the rockets must increase.
In order to understand this better it would be a good idea to look up videos about the ladder barn paradox. for example, this one ua-cam.com/video/Xrqj88zQZJg/v-deo.html .
if you want to get into more of the nitty gritty details id recommend the special relativity videos by carykh. ua-cam.com/video/Xrqj88zQZJg/v-deo.html
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
But then the rockets wouldn't be accelerating simultaneously anymore
@@lagg3sbd394 a lot of relativity confusion starts with violating the stipulations of the thought experiment.
I enjoyed the bass groove you used as bgm ❤️
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.
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?
I completly agree with that
yeah... simple answer is: It doesn't move first from it's perspective.
Neither does the first rocket.
It literally said in the video that they accelerate simultaniously at the same rate, from the same initial speed(aka same initial time dilation) HOW we got to "From different perspectives things happen before others" is just weird. Is the video talking about them being a light year apart or something ? in that case you would simply see the one in font of you start it's engines after you.... but just that. 'SEE', the string wouldn't snap or something, the system IS still accelerating simultaniously. your observation doesn't change anything
@@HaartieeTRUE dude, I don't think you understand how relativity works. Not saying I do but you don't as well
@@camperwithknife initially they don't accelerate, and just move through space, yes?
The string is under tension, between them, as they are far apart, yes?
It does not break, because they are not accelerating, yes?
From an outside perspective, this is still all true, yes?
If they are traveling with the same speed, the same trajectory, just one behind the other in its trajectory are they not experiencing the same time dilation? Where does the time dilation suddenly begin to exist? If one object moves, time dilates to it compare to a stationally frame of reference. If another moves, they can both gain the same dilation. If rocket a stays still relative to rocket b, (tho relative to earth they are not stationary) why would time be dilated to rocket a or b compare to the other? It wouldn't. If time between them isn't dilated, things CAN happen at the same time between them. So where does the sudden time dilation BETWEEN THEM, NOT 3RD OBSERVER come in? You are aware that time dilation between the 2 rockets inherently means that the velocity relative to each other changed, making the roap snap/rockets crash into each other/drift apart befor the engines even get to be activated
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…
This comment is underrated............LOL
No. If one rocket pulls the rope fast enough, it will snap. *Why?* because the rocket accelerates, while the rope is dragged by it; the individual atoms of the rope feel the force of the rocket accelerating as they are oulled by it. If you tug the rope lightly, the atoms can easily handle and the force, as the atoms at your end of the rope pull the rest of the atoms.
If you pull the rope too fast, the electric / molecular forces holding the atoms of the rope can't handle the stress, so the rope snaps. Generally speaking, you'd have to pull almost any rope with the force of a nuclear bomb in order to snap it.
@@simonwillover4175 Bruh...... We know that. He's just being sarcastic. Btw, appreciate ur thoughts though
@@simonwillover4175 obviously if you accelerate too quickly it would cause tension in the rope, but literally what is explained in the vid is that a rocket accelerating slowly enough as to not tear the rope would pull it but a second rocket accelerating at the same rate would snap the rope even though intuitively pushing against the rope wouldn’t cause tension. The effects of length contraction is what causes the tension to snap the rope which wouldn’t happen if just one rocket were pulling it.
Wow. Exactly! But just because, in a suitable frame (e.g. that of the rope), the second rocket is not pushing the rope but pulling it backwards.
No, the string will not snap for the same reason the back end and the front end of each spacecraft doesn't rip apart. If the two spacecraft tied together by the string accelerate at the same rate at the same time (from the object's perspective). they can be treated as a single (if flimsy) object. If things worked the video describes, the spacecraft themselves would in fact disintegrate because they themselves are actually made of countless seperate objects (Atoms, molecules) that are held together with "strings" (electromagnetic forces) that would experience the same phenomenon. The multiple points of acceleration are irrelevant if they are synchronized from the moving object's perspective. remember each engine isn't a single point of acceleration it too is made of countless individual objects being held together by "strings" each with its own unique bit of acceleration that combine to make up the acceleration of the whole engine.
The space between the two spacecraft will appear to have not changed at all from the spacecraft's perspective (if it did, then it would prove that there is an absolute frame of reference, which does not seem to be the case in our universe). For someone watching from a "static" perspective, the spacecraft, the space between the spacecraft and the string would all appear contracted at the same scale such that nothing will break.
The engines if they are also analysed as multiple points of acceleration, instead of single points of acceleration, will also face similar strains like the string will face for similar reasons and if the material connecting them is not strong enough , that material will also break
15 seconds into this video and my brain already shit itself
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.)
The observer on the front rocket would see his rocket start before the other one, and thus would see the distance between the rockets steadily grow.
You mention that the contraction “only occurs in a different frame”; note that because the rockets are continuously accelerating, they inhabit infinitely many inertial frames, making it quite easy to find one in which the string is untenable. All reference frames will see a breakage.
@@notme98 I should have added the 'definition' of simultaneous in my description. Afix a light bulb to the string dead center of between the rockets. Turn on the light, i ignite the rockets when the light pulse arrives. From the light bulbs point of view the rockets remain equal distant.
An outside observer that is not on a line perpendicular to the string at the light bulb would see the string grow or contract, but the observer at the light bulb traveling with it would see the string's lenght remain the same. No string breakage.
@@eldencw I've been noticing that most of these people do not understand that when 2 objects are stationary relative to each other, there is no time dilation between them.
@@eldencw An "observer at the light bulb traveling with it" does not inhabit an inertial reference frame, as he/she would be accelerating; thus special relativity does not apply.
@@notme98 correct! since the engines, and the light bulb travel at the exact same acceleration, they have the exact same inertial frame of reference, thus no time or length dilation.
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
String is assumed massless
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.
This was an interesting piece of information to put into my braincase today.
At the beginning you said that the two rockets accelerate at the same time by the same amount then later you say they don't? You need to be consistent because it seems that what you are implying is that even if you are absolutely perfect the string would still break when it shouldn't when viewed by the second perspective.
" _At the beginning you said that the two rockets accelerate at the same time by the same amount then later you say they don't_ "
They accelerate at the same time in one frame, they dont in another frame. It is called relativity of simultaneity. Events that are simultaneous in one frame will in general be non simultaneous in another frame
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.
Yeah no, it's no paradox to begin with haha. It's a misused term
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)
I think you're overlooking that relativity is relative. The spacecraft and string don't actually shrink from their moving point of reference. They only appear shrunk from a different (stationary or much slower) point of reference. From the spaceship + string's point of reference, it is the stationary observer who has shrunk in length. There is no real change in length; only apparent change in length from the viewpoint of an observer at a much different speed. From.thst different point of reference, the entire spaceships-plus-string system will appear to measure slightly shorter, despite the fact that if you were to measure them from within their own moving reference speed, you would detect no change in length. The string does not break.
It’s crazy how you can like and comment before you even see the video
Premiere, ditch it, never again
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.*
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 :)
That's how I see it too.
69 yay
12 nay
Looks like premier mode is a no go unless content is interactive.
Having an unwatchable video in my subscription feed is always fun and exciting!
@@pafnutiytheartist Just forget it, he was experimenting
Its more that its a short video, if its a big project i can appreciate a premiere
@@pafnutiytheartist 😂
“What I told you is true, from a certain point of view” thank u for the explanation Obi-Wan
Yep, I can never hear that phrase and not think of that scene! xD
I think about the spaceship paradox often and now I'll think about it even more. thank you... ^_^
Very happy to have guessed that the answer would have to do with relativity of simultaneity.
"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"
Because whether two events happen at the same time or not is also relative, so if they accelerate a the same time from the stationary observer's perspective, they generally accelerate at different times from other perspectives
Time is relative. When you're moving fast, you get a different perspective on time. If the rockets fired at the same time according to a stationary perspective, they had to fire at different times from a moving one. Granted, those different times are probably not as exaggerated as was shown in the video, but that was just to make things clearer.
Good question though!
Special Relativity showed that time dilation makes "simultaneous" relative too. Observers in reference frames moving at different speeds can observe two events occurring in different orders.
The accelerations are not simultaneous in the moving object's frame of reference.
thanks everyone. I framed my question poorly. both rockets start out in a stationary frame of reference. which, should mean that a "Simultaneous" firing should maintain its synchronicity between the perspectives of both rockets. so, if the switch between a stationary and moving perspective occurs simultaneously, then the sequence of events should be consistent across all reference points, no?
I had a whole homework on this exact problem for intermediate astrophysics, this was like a pleasant PTSD attack now that I'm graduated and someone else is explaining it
"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
for some reason youtube does not recommand me ur videos anymore im triggered i need my minute physics
Exactly the anti-clickbait Derek talked about
I think it's Derek*
en.wikipedia.org/wiki/Derek_Muller
@@Vagabond-Cosmique fair enough
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?
Star trek doesn't have thrust, acceleration, and relative movement correctly described. In their universe, a constant thrust doesn't equal a constant acceleration, instead it equals a constant speed, like an earth vehicle moving through a fluid. Plus the use of polarized hull plating and shields generally negate the force of hull pressure while the saucers tend to have a docking system that can bear a slight amount of stress as well.
In our universe, if you were to fire jet (or impulse) engines while in our atmosphere, you would only travel to the speed at which the expanding gasses travel out of the engine, subtracting friction. Let's call that 420fps. In the reduced friction of space, the inertia of a craft traveling at 420fps will _make it so_ the craft keeps at constant velocity. But the added thrust, if you were to _engage_ the engines, will accelerate the craft further above 420fps at a linear rate equal to force of applied pressure divided by the mass of the craft.
At warp, in either universe, the entire craft remains inside a bubble of relatively stationary space, contracting the space ahead of the bubble and expanding the space behind the bubble, so the nacelles are not actually providing thrust.
Obviously the Q, the traveler, Tom Paris, Guinean's misinformed racial opinions, the Borg, subspace transmissions, Wesley's inability to shut up, temporal loops, Faith of the Heart, Tasha Yarr's emotional scars, the beast at Tanagra, and wormholes are all excluded from anything that makes sense.
Also man, I am loving the upright bass score!
Finally the OG minute physics
Aren't the two rockets (and the string) in the same inertial frame at all "times"?
Yes they are. Therefore, this is nothing but fantasy...
they are and that is why this video is 100% wrong ofcourse
Imagine both rockets at rest, a light source from the center of the string sends a signal to both rockets and when the rockets see the light signal, both would immediately start traveling. In the rocket’s rest frame, both rockets receive signal at the same time, because light signal has the same distance to travel in both directions. However, in a moving frame with velocity v to the right, the rocket on the right would receive the light signal BEFORE the rocket on the left, because in this frame, the rocket on the right is moving to the left, and is “meeting” the light signal, while the rocket on the left is moving away from the light signal and thus would receive the signal later. The start of rockets are said to be separated in space time by a space-like interval, which means that two different observers may disagree about the order of the two events in time.
@@dantong5623 Nope. If the 2 rockets are accelerating then you are correct. Relativity clearly states that if these 2 rockets are in the void of space with no other gravity influencing them, there is no way for them to know if they are at rest or moving. The only thing they can do is compare their state to the other rocket. This is where most people get tripped up. Again, a body can only know 2 things about itself. 1. Is my velocity changing? (Inertia) 2. What is my velocity compared to the objects around me?
And so the rocket on the right would enter a moving frame sooner, according to observer moving to the right, than the rocket on the left does
If both rockets and string are accelerating the same they should all behave as a single object and the string won’t snap. But they have to accelerate at a rate that the atoms can maintain the momentum. It’s like when a train leaves the station and you are standing.
No, because of time dilation the front rocket will always appear to „start“ earlier, resulting in a snapped string.
It‘s counter intuitive, that‘s the whole point ^^
@@MisterK9739 Nah, you can easily sync two rockets to start at exactly same time - just sent a beams of light from point in-between to each them.
@@artyommnoromin1035 But there is no light source in between these rockets. You just altered the experimental setup and then say it gives different results. Yeah no shit
@@artyommnoromin1035 The purpose of the thought experiment is to clarify the stretching of space due to acceleration. So your "what if you time your acceleration in such a way that you compensate for the stretching of space by the front spaceship" argument is counterproductive.
It can be considered a different situation. (the two spaceships are always tied by a rope)
In each frame the length of the rope has a different value (the speed of the two spaceships is initially the same in each frame), and obviously in the frame of the two spaceships the length of the rope is the maximum length. (in this frame the two spaceships and the rope are stationary)
In the other frames the length of the rope is shorter, because in the other frames the two spaceships and the rope move at a constant speed. (in these frames the length of each spaceship is also shorter)
I now consider the two events A and B,
A: the leading spaceship accelerates
B: the second spaceship accelerates
If the events A and B are simultaneous in a frame F (only in the frame F) the rope contracts (the speed of the rope increases but the rope does not break in the frame F), and the length of each spaceship also contracts in the frame F.
Instead in some frames the rope breaks (if in these frames the event A occurs before the event B), and in my opinion in this case the situation is problematic.
you're analysis broke when you said "in this frame the two [ships are stationary]"--which is early on.
Each ship sees the other moving away as they accelerate.
@@DrDeuteron If the two events A and B are simultaneous in F frame ... it means that the two spaceships accelerate simultaneously, and in my opinion the rope does not break.
If the speed increases then the rope contracts and the two ships become smaller, but if the two ships in the F frame accelerate simultaneously ... the rope does not break...
THIS! this video right here, the one we all just watched, is the reason i went with biology and not physics as my career