The Barn Paradox: A Dilemma of Relativity Explained

In this video, we are going to solve the famous barn-pole paradox also called the ladder paradox in Einstein's special relativity. This paradox arises with a naive use of the length contraction phenomenon in special relativity (similar to the clock paradox using time dilatation) which is simply resolved using relativity of simultaneity which shows (again) that we can never use just one phenomenon alone and we have to use the whole theory of special relativity.
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[@lukasrafajpps]

If you enjoyed this video you can buy me a coffee here www.buymeacoffee.com/pprobnsol Much appreciated :)

[@theCodyReeder]

When he says "the price you pay is the life of your friend" he's not kidding. If your friend is not made of indestructible materials, like the car and garage, they are going to get absolutely plasmized! Like they will get hot, having nuclear reactions up through fusing carbon and nitrogen, hot. When changing speed that quickly they would be vaporized more than if they were inside an exploding thermonuclear bomb.

[@theCodyReeder]

I was wondering, does this have anything to do with how well neutrons are captured depending on their speed? Their target shrinks when they are moving fast! Right?

[@lukasrafajpps]

It can have an influence but it has more to do with the potential created by the strong-forece inside the nucleus. For example for U235 slower neutrons are captured much more easily because when they get very close to the nuclei they get captured in the potential well having not enough energy to escape whereas fast neutrons can escape back from the potential well.

[@eckee]

nah, they will have airbags they'll be fine

[@undercoveragent9889]

But if the car is front wheel drive, in order to length contract, the rear of the car would have accelerate at a faster rate than the front does. Therefore, if the front is traveling at the speed of light, the rear will be traveling _faster_ than the speed of light.

[@titastotas1416]

I have seen this be explained many times yet this one it the first to lay it out in such a way to not leave any questions unanswered. It is impressive to me seeing how you fit this concept inside a 5 min explanation without a having to rush it.

[@lukasrafajpps]

thanks! :)

[@biocronics]

I have no idea how I stumbled accross this video, but, well done. Great explanation.

[@lukasrafajpps]

Thanks, I am glad you liked it :)

[@kryten88]

That would be the KZbin Algorithm Paradox

[@fabiomazza4058]

Very clear explanation!

[@ChaseNoStraighter]

Nice video. I am a bit troubled by the second example as it is no longer a inertial reference frame due to the rather large acceleration. There is a rotation caused by acceleration that should be part of the story. Your two observers in your story see the action in the last to close door, the ground observer sees the door closed and then opened part way while your friend sees in only partially close.

[@thibautklinger5178]

I did a few calculations on how this would Look from the garages perspective. What I found was that If WE choose the Velocity such that the car and Garage length are equal from the garages POV the Doors Close at the Same time but the car will Not Stop at once. While the Front might Stop instantly, the Back will still move untill the information reaches it. This means the car seems to contract even more now. Therefore the Front Doors closing and the Back of the car stopping are Not simultanious in the Garage frame. I was about to Look at it from the Cars POV but I could Not find the time for a propper Lorentz transformation yet. Please let me know what you think sofar

[@bvr-rel]

This is a nice and interesting video. However, I think there is a problem at 5:00 where the situation is shown from the reference frame of the car's driver. Thus the car is at rest (and not contracted) while the barn is moving from right to left and will hit the front of the car. But the video shows the opposite, as if the car is moving and therefore, the back of the car keeps moving when the front is stopped. That's not a correct description.

[@lukasrafajpps]

Yea there might be a consusion because the camera stopped as the video slowed down. good point should've been more thorough.

[@rre9121]

Is it infinite? Wouldn't it be whatever the lennard-jones 6/12 potential would indicate?

[@kucher7778]

great content

[@prajapatikaushik6674]

you just blown my mind

[@lukatolstov5598]

2:34 You must draw doors contracted like the environment, but when door closes it becomes normal.

[@sergiolucas38]

Good video, thanks :)

[@xcoder1122]

"How could you able to close both doors at the same time" - is the answer to understanding relativity. There is no such thing as "at the same time" unless it happens at the same place. You cannot close two doors at the same time that are apart from each other, no matter how little they are apart of each other. You can close them within a micro fraction of a second but when something moves close to light speed, a micro fraction of a second is an eternity! When you flip a light switch, all lights go bright at the same time, right? Wrong. They go bright one after another but it happens so fast that for you it looks as if it was at the same time and even for a slow-mo camera it still looks that way but that's not what is happening. And if the effects of two distant events really hit you at the very same time, then this is pure coincident: Those events were then neither related to each other (one cannot have caused the other one), nor would they have hit you at the same time if you had been standing in a different spot (e.g. just one step closer to one event). As soon as you realize that at the same time is just an illusion, relativity loses a lot of it's weirdness and things start to make sense again.

[@ethribin4188]

What many dont understand about length contraction, is that atoms dont move closer, or further appart from their point of view. They are the same distance from eachother, even with space deforming.

[@lukasrafajpps]

I wouldn't say it is space deforming but with movement simultaneity plane rotates and if you want to measure length, you have to measure the positions of two points in space simultaneously. But since there is no absolute simultaneity in special relativity, the definition of length breaks up.

[@orcmanddegormak1031]

id say, if one applies length contraction to the car, relativity demands it be applied to the barn as well, thus the barn being smaller than the car implies the car can never fit into the barn. volumes arent changing, there is only the illusion of change.

[@lukasrafajpps]

But that is not correct, only observer stationary relative to the barn can apply it to the car and only observer stationary to the car can apply it to the barn. Clearly there is something wrong with quantity called length in special relativity and it is due to the fact that there is no absolute simultaneity. I have a dedicated video about length contraction where I explain how the definition of length breaks in special relativity kzbin.info/www/bejne/p2iTlZptgJuXhNU

[@orcmanddegormak1031]

@@lukasrafajpps but it actually happens... regardless of weather or not the math says it does or doesnt.

[@massimilianodellaguzzo8571]

Nice video, thanks! (This paradox is very fascinating) I like to imagine a swimming pool instead of a garage. (and there are no two doors) Does the car fall or does it not fall into the water?

[@lukasrafajpps]

Hi, well, nice thing is that you can choose any reference frame and solve the problem there and physics must be the same in other frames. From the reference frame of the pool, it is obvious that the car would fall into the water therefore it must also happen from the reference frame of the car. Now it only depends on the interpretation of the car but if it was made of two atoms like I showed in the video, then the front atom would start to fall first no matter the strength of the material the car is made of and it would hit the wall of the pool the back atom would not know this (it is causally disconnected) and would continue to move and eventually would also fall into the pool. Thanks for the question :)

[@massimilianodellaguzzo8571]

@@lukasrafajpps " Now it only depends on the interpretation of the car but if it was made of two atoms like I showed in the video, then the front atom would start to fall first no matter the strength of the material the car is made of and it would hit the wall of the pool the back atom would not know this (it is causally disconnected) and would continue to move and eventually would also fall into the pool. " : Okay thanks!

[@Blameberg]

2:47 😂😂😂 I died too. From laughter

[@rolandrogerlogo4283]

Because of these space-motion relations the bending of space and time, which is a function of motion, is only possible when coming closer to the light speed limit in the physical space realm. That means if the length contraction really is true, then the length of one meter, measured on the surface of earth should be different than 400 km above the surface in outer space. This would prove that my assumption would be wrong, and the length contraction would be right. Otherwise, the length contraction equation would need some corrections.

[@lukasrafajpps]

Well, it is kinda more complicated than that, The length contraction is a phenomenon where different observers don't agree on a distance interval in space between two events assuming they measure the distance with the same instrument. It means that the distance is space is a relative quantity the same like velocity for example. There is no objective way to determine the true distance between two events. The most convinient way though is to ask what is the distance for an observer that is stationary relative to those events.

[@kylelochlann5053]

The curvature of the gravitational field is irrelevant.

[@david_porthouse]

The car is necessarily an elastic object with a shock wave travelling through it when it hits the door.

[@lukasrafajpps]

Yes, In relativity nothing can be infinitely firm just due to the fact the causality travels at a finite speed.

[@rolandrogerlogo4283]

This paradox shows clearly what happen when coming close to the speed of light and why the car is getting smaller in size if it moves close to the speed of light. There is a simple explanation about this phenomenon. First we have to know that within the universe there are space realms with higher speed than light. What happen when we expand our speed of light c? The size of our atoms shrinks automatically because the next space realm with higher speed of light is ruled by smaller atoms. That means the atom structure inclusive its substructure is much smaller than atoms in the c-spectrum. The smaller the atoms, the faster they can move and the finer is its medium or space realm. Hyperspace realms have much faster motion than our common c-realm and its atomic mass particles are much smaller. There is a relation within the universe which rules size and motion of its particles in different space spectrums. That means D3-space can have many faces depending on its motion value which can go up to 147 times the speed of light c.

[@lukasrafajpps]

Special relativity totally breaks when we cross the speed of light. It is apparent form the transformation rules where you have 1-v/c in square root which would be imaginary number when v > c. Where does this hypothesis come from? and how did you get the number 147?

[@ethribin4188]

Things like this show that time is not iys own thing. But an expression of movement through space.

[@lukasrafajpps]

relativity teaches us that anything that depends on the reference frame of the observer is not a real quantity. Time therefore on its own has no meaning without the full picture of spacetime. There is no absolute simultaneity either and therefore it is impossible to properly define quantity called length in special relativity as well.

[@titastotas1416]

It is ok I have an infinitely durable friend.

[@kittysplode]

what you've done isn't park a car. what you did was set off a bomb. you can park the car the same by crushing it with matter, no universe-shaking explosion necessary.

[@hurmzz]

He can fit in the barn when traveling fast enough but obvioulsy he can’t park in there.

[@lukasrafajpps]

He can provided the sufficient strength of the materials the barn and the car is made of but of course in real world no way

[@hurmzz]

@@lukasrafajpps There is no strength sufficient near light speed. As soon as the car touches the door (at least) atomization will happen. And also if there was such a thing. The car is only smaller because of it’s speed. When it is standing still it does not fit.

[@rattiusr6418]

Does this mean the person inside the car would start to visibly see the car start to squish as he crashes into the front door?

[@lukasrafajpps]

Well, it is quite difficult to imagine what he would see but when I try to imagine it in my brain I would say no. The comunication among nearby atoms happens at the speed of light so until the light from the front atom reaches you all of the atoms in the car are already stationary including the one that is closest to you possible.

[@rolandrogerlogo4283]

My knowledge about the max light speed value of 147 times c is from recordings we have since 1975 by constant communication with alien scientists from the Plejare Civilization who travel space for hundreds of thousands of years. Far away they are our ancestors and have some relationship since humankind is on planet earth. This is also the reason they look the same as people on earth. there is a lot to learn from them even if they do not want to interrupt our evolution in technical standards and keep silent on many topics. The theory of relativity and the Lorenz relation breaks down if we confront the speed limit of c. That is why special relativity has limits and needs an extension to be presented properly. I am working on some reference books with only german translations. There are more data on the right concept and structure of our universe coming out soon in a new book in English. The real universe structure will show the intrinsic principle for the real quantum realms and spacetime relations.

[@PADARM]

I think that most of the supposed paradoxes have no basis in real life, for example, no car is going to stop instantly at that enormous speed without a huge inertia.

[@soup9242]

Is no body going to mention that that car is going at 94% the speed of light?

[@lukasrafajpps]

you have calculated it based on the rate of contraction? :D

[@soup9242]

@@lukasrafajpps No, based on another video of the same paradox.

[@tnwhiskey68]

Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality. The scientists from Franklin to Morse were clear thinkers and did not produce erroneous theories. ~Nikola Tesla Absolutely applies to this absurdity!

[@dannywhite132]

The thing that will never cease to piss me off about a lot of relativity theory is that we will never (in my lifetime anyway) have the capability to truly test things like this, meaning that whilst tbe theory makes sense, I'll never practically be able to see a car of infinite rigidity drive at near light speed into a garage and both stop in and not inside its borders

[@silverrahul]

relativity was already tested before your lifetime.

[@lukasrafajpps]

yes you can't explain such scenarios but those are just for explanations of possible paradoxes. You certainly have a ways to prove relativity differently.

[@joecitizen3955]

Not much of a 'friend' to risk life like that? Who was he anyway? The 'Flash"? (light barrier be damned! Help me out Gravity at Planck!)

[@scientificallyliterate7462]

This is not the barn-pole paradox. This is car-in-the-barn paradox.

[@lukasrafajpps]

As a physicist by heart I don't see a difference between a pole and a car :D but yes you are right thank you :)

[@VortekStarling]

Can you solve this problem? To explain how 2 laser beams going in opposite directions from the middle of a moving train car to clocks at each end could appear to be moving at the same constant speed in both directions to an observer on the ground, Einstein suggested that the clock at the rear would show a time ahead of the time on the front clock from the observer's perspective, although they would both be moving at the same rate due to moving at the same relative speed. Both clocks would be behind the observer's clock, due to time dilation, but the front clock would be behind it by more than the rear clock, in Einstein's mind. The question is how did the two clocks come to vary from the observer's clock by different amounts in the first place. Einstein never explained that, because he couldn't. It's the same Lorentz Transformation factor for the entire train car and the entire car accelerated at the same time and rate so how did the two clocks come to vary by different amounts simply by being at different ends of the train car? You can't answer it because nobody can, because Einstein's theory is flawed.

[@lukasrafajpps]

This is a clock synchronization problem. If you have two cocks separated by some distance and you synchronize them in one reference frame, then they won't be syndronous in any other frame that is moving relative to them. Don't do the same mistake as many people do being too phylosophical about this. Special relativity only has two postulates from which one of them serves just as a reality check which is the first postulate that physical laws should not depend on the inertial reference frame you use. The second postulate is that about the speed of light and now you have to manipulate space and time in such a way these postulates hold and it is indeed possible. In this scenario, it is by the relativity of simultaneity. You basically force the simultaneity of events in such a way your two postulates hold and that is everything there is to this problem. In translation this means that if in one reference frame you have those two clocks synchronized, then by enforcing the two postulates you calculate how the clock differ in other frames. Please don't ever try to do the logic in reverse. I also made a video about relativity of simultaneity that explain a lot about this problem so feel free to check it out kzbin.info/www/bejne/iYeZnq1-fZlknc0

[@renedekker9806]

_"Einstein never explained that, because he couldn't."_ - Einstein did explain it, he specified in details how clock synchronisation works. Don't make the mistake of assuming something must be false just because you don't understand it. _"...the entire car accelerated at the same time and rate"_ - not according to the outside observer. If the front and back of the train would accelerate the same amount at the same time, then the train would be ripped apart (Bell's spaceship paradox). And after acceleration, the clocks need to be resynchronised anyways, because they go out of sync.

[@VortekStarling]

The desynchronization seems like a convenient way to get around the flaws in the theory. You didn't mention anything that makes it seem logical to me, it just seems like more far fetched rationalization.@@renedekker9806

[@silverrahul]

" _It's the same Lorentz Transformation factor for the entire train car and the entire car accelerated at the same time and rate so how did the two clocks come to vary by different amounts simply by being at different ends of the train car? You can't answer it because nobody can, because Einstein's theory is flawed_ " look at the lorentz transformation equations carefully. There is a x-coordinate term in it. So, being at different ends of the train matters. The two clocks have different x-coordinates, so naturally, the lorentz transformation will give different values for them

[@VortekStarling]

Suffice it to say that it's impossible for the same offset in readings between the back and front clocks to work with a horizontal light beam AND a diagonal light beam at the same time. That's why you will never find a description of such a scenario anywhere, even though it's an obvious thing to do if the goal is to show how Special Relativity is valid. Wouldn't some scientist be like "look at this, it even works with a diagonal beam from the upper back corner to the lower front corner of the train car at the same time as a horizontal beam from the LOWER back corner to the same lower front corner"? I invite you to do just that, make a drawing of it with a geometry program and upload it to an image hosting site and provide a link to it, or however else you want to show it, a video or whatever.@@silverrahul

[@RichardASalisbury1]

Still confused.

[@lukasrafajpps]

maybe watch my relativity of simultaneity video

[@Jaggerbush]

This is a messy explanation 😬

[@KeianhhnaieK]

Special relativity was disproved a very very long time ago. It's sad people still repeat superficial junk, but that's because superficial people understand superficial things, rather they pretend to.

[@rickymcriver]

Completely agree! Earth is a dinosaur, our universe is a Cristal Ball from Batman, and today I had a dream were I could fly, therefore, human beings can fly!! We are the real scientists 😎😎

[@renedekker9806]

Indeed. Superficial people repeat superficial junk in KZbin comments, such as "special relativity was disproved". It's because superficial people only understand superficial things.