Can You Solve the Spaceships Paradox?

here's a question say you have two spaceships identical side-by-side connected by a string in outer space then at the same moment both pilots identically accelerate they get going so fast they get close to the speed of light my question to you is what happens to the string connecting those ships will it stay intact or will it snap I know Aria knows the answer she has a lot of processing power from somewhere I don't know but I want you to really think about the answer for a second just take a second so how about this spaceman yeah it really is okay do you have an answer good me too but I guarantee mine is a lot more complicated now entering the facility if two identical spaceships accelerated identically connected by a string to relativistic speeds you would see them blast off into the cosmos and then at some point the string would snap this presents a paradox Bell's paradox in fact there is no apparent reason for the strings snapping there's no apparent force on it it's as though the ships are getting further and further apart as they travel but we see them staying the same distance apart what is going on here well to answer that question fully we have to get basic like even more basic than a North Face jacket of boots you know who you are basic like space-time where are you right now you're probably at home which resides within a country I'm willing to bet which is on a planet called Earth I'm just guessing which is in the Milky Way galaxy hmm and maybe within the observable universe call it a hunch but how would you show me where you are in space-time well let's graph it using what's called a Minkowski diagram so let's have two axes Y an x on the y axis we have time and on the x axis we have space now if you were to graph my position right now in space-time from my perspective I'm not moving so I would appear as a vertical line I'm not changing in space I'm only changing as time goes towards the future up and up if I started moving at some constant velocity my line would shift to look something like this these are called my world lines or possible world lines they describe where I can be in space-time but of course I can't go anywhere in space-time because there's a hard limit on how fast I can go the speed of light if we add that limit to our diagram say a dotted line at 45 degrees to make it easy we now have a light cone that acts as a boundary for all my possible world lines this defines every place every Kyle could possibly be past present and future now without getting too complicated if you were to start moving really really fast and approach the speed of light your space-time in these diagrams would warp to accommodate the unchanged ability of the speed of light in all reference frames and this warping is actually the key to solving this paradox wait what Kevin did you did you fix the locking mechanism on this thing yes Aria I'm not moving very funny there we go hey guess who's feeding the snake to pusses for a month take a wild guess Kevin when I'm not moving you and I will observe the same thing nothing weird going on but once my facility hyper rail starts approaching light speed our observation of each other will start to diverge from your perspective I will begin just slow down if you were to look at my watch it would be ticking more slowly than your watch and from my perspective you look all sped up and totally ridiculous you see changing space-time adds a relativity to perspectives as mind-blowing as all of Einstein's ideas are this simple fact underpins at all now Aria could you decel this thing with inertial compensation this time thank you the custodial staff really doesn't like a cleanup oh you mean that time I stopped so quickly that their bodies basically yes yes that's what I mean yes relativity and disagreements about what now means between observers moving differently like our watches we're getting different times brings us back to our space-time diagrams and the paradox I have a shiny new toy as does Aria I'm absolutely snatched she totally is so we have a normal nonrelativistic space-time diagram now let's add the world lines of our two ships accelerating they are curved lines because they are accelerating now notice from our perspective the ships in their travels are always the same distance apart the paradox strikes again if they're always the same distance apart how could a string possibly snap you say well let's dive in into my fresh to death right now we see the ships from our perspective but what do the ships see when they look at each other relativity as we discussed could make their views very different well when we do the math for how the first ship spacetime would shift at a relativistic speed we find a new space-time envelope if you then ask the first ship to observe where the second ship was at some time they agreed on the next spot on the world line of the second ship where it meets with the space time of the first isn't at that equal distance anymore it's way up here shortly after launch the pilots of these space ships would report to an outside observer that they were moving further and further apart from each other at different speeds and of course this increasing separation would put some force on the string eventually snapping it paradox so oh nice or is it come on I was moving the thing is the length of our string really what we're showing with our fancy space-time diagram or is that also relative don't feel bad if you didn't initially get the right answer to this paradox reportedly the guy who thought of this Gedanken experiment posed it to a number of his colleagues at CERN to some of the smartest people in the world and most of them got it wrong too scientists themselves they will tell you they might in fact be one of the easiest groups of people to fool because they relies so heavily and unthinkingly sometimes on their expertise heck one guy fooled all paleontology into the inky and found the missing link and they didn't figure out he was a fraud for four years you are all human and you always have to stay vigilant for any unintuitive trickiness and especially wait we're Emma this is totally fun I definitely know definitely know where I'm going I take it lift it wait how can a Street intersect with itself now we're on to something now yep now we're on to something another sushi please here we go here we go did you get lost again yeah well I wasn't spawn stand thought yes come on just let me impede the warping of space-time is weird and art diagrams imply there should be some weird warping and stretching of the string as well but this isn't true and this is where I find a lot of common misunderstanding about how relativity works there is no physical change to an object when it gets really really close to the speed of light if I were to blast off from your perspective yes I would slow down and even concurrent but if you asked me what I was observing everything's totally normal you see the transformations that you learn about in physics class are just relativistic pictures a way for the universe to translate the space-time of one observer into the language of another so we have our paradox again two ships identical accelerating identically to near lights be connected by a string after they accelerate they will report each other moving away at different speeds and the stress snaps the string at no point is there any physical change to the pilots to the ships or who's flying that other ship or to the length of the string it is always the same length it has to be it just breaks because there's an effect two spaceships fighting over it all of this even though it seems impossible for this to happen from an outside perspective paradox solved or is it Jay King Symons here's another way to think about this whole situation without all the fancy space-time diagrams so imagine two ships again but this time they are moving away from you as we move away from who is flying that other ship as we move away from you we should get smaller and smaller from your perspective right we have to if the ships were going further away from you and stayed the same distance apart the whole time that wouldn't be possible unless they were moving apart from each other as they did so similarly the only way the space ships in our paradox can remain the same distance apart during travel as space time warps is for them to actually separate in a different frame of reference relatively speaking paradox solved for realsies until next time the space weather is nice today though that solar wind thank you so much for the very nerdy staff at the facility for their direct and substantial support in creating this video today I especially want to recognize research assistant bells of DOC destroy of Lark on five that's not his real name I don't know if you can tell that and visiting scholar Clayton Odum if you want to join the facility if you want to join our patreon and our discord where right now over a thousand nerds are giving the episode ideas sharing pictures of their cats talking directly with me organizing their own trivia nights you can go to patreon.com/scishow and I cannot thank you enough there's more and more of you each week and I don't know how to pass that a lot of these Gedanken experiments assume that you can just travel at the speed of light or close to it wouldn't be cool if you had a Lightspeed spaceship well yes but there's space is not a perfect void like my heart and there's still particles in it like hydrogen and if you were to go close to the speed of light even in space you'd hit enough of these particles with enough energy that it effectively irradiated you and you would be fatally irradiated which is fun to say in under a second which is not fun to have happen to you oh it's don't more names okay cool thank you cool cool cool thanks for watching

Channel: Kyle Hill

Views: 571,090

Rating: 4.854146 out of 5

Keywords: because science, engineering, kyle hill, learning, math, physics, science, stem, the facility, special relativity, problem solving, space, lightspeed, spaceships, bells paradox, spaceship paradox, time dilation, kyle hill channel, rokos basilisk

Id: 5iBtHroB978

Length: 11min 24sec (684 seconds)

Published: Thu Jun 25 2020

Reddit Comments

[u/juggernautjefe81]

Oddly enough I am currently watching this video in a minimized window and scrolling through Reddit to see this and be first! Lol