@@oatlord He's probably taught it a bunch of times. I know both of those paradoxes were both in my Modern Physics textbook in the end of the 1st or 2nd chapter. I'm guessing they're pretty common for textbooks. Mine had quite a few. I also remember one with someone running at relative speeds with a ladder towards a shed that is too small to contain the ladder XD It's similar to the train one.
@@oatlord Oh, and they also like to include one with twins and one gets sent off a near the speed of light to a distant star systems and then turns around and comes back. The cool part is where they send happy birthday messages to each other and how sometimes they seem too slow and sometimes they seem too fast between birthdays :P
I remember this question being in a physics exam I did 5 years ago. I answered it differently... but I still think it holds merit (I did well in the exam but no idea if I got this bit right - maybe someone can tell me?)... So from the point of view of the train driver at the front of the train: - when he is midway through the tunnel, he sees the tunnel in front of him Lorentz contracted, but behind him the other half of the tunnel is lengthened - he still sees the guillotine miss both ends of his train because for him, the guillotine comes down when he is very close to the exit
I still don't understand what decides that the other guillotine comes down first. Mind-blowing indeed. I guess I should ask this: what if there were two tracks and two trains going in opposite directions, and they were inside the tunnel at the same time? Would they have contradictory opinions about which guillotine came down first?
The first one coming down first is because if you are moving towards the guillotine, the light from guillotine hits you first, so you think that event occurred first. To answer your second question with 2 sets of tracks, yes, people on different trains will have a contradictory outlook on what occurred first
What'd happen if you were to place a very long surface (like a long wooden plank or something) resting on the top of both guillotines with a bowl with any liquid; in such a manner that, if the guillotines are not both at the same height at the same time, the plank won't be leveled and the water will spill. From one perspective the water wouldn't spill because both blades fall and rise at the same time without chopping the train off. But from the other perspective the water would spill because they don't fall at the same time; and quoting from 5:22 that's something that has to be agreed upon because either the water gets spilled or it doesn't, since it's not a matter of perspective.
Could we get a Numberphile video or something that focuses on the maths behind this? I'd quite like to hear more about that, because if it's as simple as Prof. Merrifield here makes it sound, I might be able to figure it out myself.
The last 5 seconds of the video... I have my headphones on full volume, I go to put my laptop down, and I think the video is over... and all of a sudden I hear a guillotine snap down hard. That scared me out of my mind.
The math, as they say in the video, really is relatively simple. If you want a complete understanding of the topic, I highly recommend googling it. If you have any questions, try reddit or stackexchange.
+Alex I Yep, very simple math. Trigonometry. I can't even pass Algebra for crying out loud. And is sad because I really love physics but my brain cannot do math properly.
+Bassotronics I'm exactly like you I love listening to university courses, listen to books, I love it but not smart enough to understand a lot of it, there's one video with mark leweldin not exactly the way it's spelt, but you should watch it it's on RUclips, it's his last university course, it is awesome.
I'd love a response to this from someone on or behind the camera. Couldn't think of a particular video where this comment would've been more 'correct', I like this channel. Anyway, I was an IT instructor for quite awhile, could easily still stand up in front and do some teaching. Here's the ONE THING I always thought would give the 'rubber sheet' gravity graphic greater value as a visual aid. Draw AT LEAST TWO rubber sheets, offset from one another, specifically to 'break' the mind's capability of abstraction of the habit of thinking in only three dimensions. Since every graphic of the solar system ever drawn appears as an extended elliptic ("The axis of rotation is NOT perpendicular to the plane of the ecliptic."), people tend to incorporate that little bit of trivia into their 'new understanding' of how gravity works, once they've finally seen the 'rubber sheet' graphic. But the 'single rubber sheet' fails to specifically illustrate that the curvature of spacetime around a massive object, (BTW, the spell checker shouldn't redline the word "spacetime", Google. Shame on you!), it fails to specifically illustrate that the curvature of spacetime around a massive object is totally xyz-coordinate-independent. It curves in all possible directions, related best to some gravity-influenced object by showing that it is vector(?) dependent. Whichever direction the approaching (or orbiting) object is in relation to the other object, THAT will affect what vector(?) the two bodies will respond to each other 'in'. I think this would be MUCH better illustrated by including at least TWO exemplar 'rubber sheets' in every graphic depiction of same. Just my opinion. Would love to hear the Professor's opinion. Please forgive the probable misuse of the term "vector", although I'm pretty sure you know what I mean to say.
If I ask, then, "what really, exactly, absolutely happened?" the answer would be, "it depends on the reference frame" ? So it's like saying that reality is relative?
Leif Urdaneta Not really. Reality isn't relative, but our *perception* of it is. The question of what "absolutely happened" makes no sense, because we're only talking about how people moving at different velocities perceive spacetime from different perspectives. In the example of the train, separate inertial observers will disagree on the time the blades dropped, the length of the tunnel vs. the train, and the masses of the tunnel and the train - but they will always agree that the train passed through the tunnel unharmed. Let's say I draw a chalk circle on the wall in front of me. I ask you, "Do you like my circle?" But you're standing a few feet to my left and viewing it at an angle, so you say "It's not a circle, it's an ellipse!" Then our friend leaning against the wall says "It's not a circle *or* an ellipse. It's just a line!" All of our perceptions are "correct" - there's nothing special about my perpendicular angle that makes a circle the "right" way to see it - we're just seeing the same thing from different perspectives. And at the same time, our different perceptions don't change any facts about reality - no matter what angle you're looking from you'll never see the circle as, say, a square or a triangle. That's essentially what's going on in special relativity. Changing your velocity changes your perception of time, distance, and mass by changing your perspective in spacetime, but it doesn't change spacetime itself.
Exactly. To the observer near the tunnel the train would stretch out as it decelerated. And for the people on the train, they would stay the same while the tunnel and the rest of the outside world stretched out.
Oners82 I guess it depends on how you define "reality," but imo, "reality is relative" is a bad conclusion to draw from SR. Like I said before, in the train example there is no observer that will see the train get cut in half while another sees it safely travel on. The overall outcome of any situation will remain the same for all observers. "Reality" is preserved in that sense and is certainly *not* relative. Otherwise, we'd have paradoxes coming out of the woodwork. All that's relative is time, distance, and mass, which warp depending on your velocity. Those are "real" effects in the sense that you can measure them, but you can measure the warping of regular 2-D perspective too. And even though, say, a ruler looks shorter when I view it at an angle, we never say the ruler *is* shorter when I view it at an angle. We understand that it's an issue of perception due to my relative position to the ruler. SR is a little more far-reaching in its claims, but it's essentially the same thing. And I think it's easier to understand that way.
I think you're just not listening to what I'm saying. Which I don't blame you, considering these are RUclips comments, but the question was "Is reality relative?" And I say no, it isn't. Despite the fact that two observers in different inertial frames disagree on the simultaneity of events and the lengths/masses of objects, they must agree on *everything* else, and even their disagreements must be symmetrical. I'm not saying the effects of SR are just illusions, or that there is any "correct" reference frame. I'm saying that all observers experience the same "reality," just warped and skewed based on their relative velocities. It's more of a philosophical point now that I think about it, but I still think it's an important distinction.
RoboBoddicker So just imagine this one: I'm going from earth to mars with a rocket. But I'm going at a speed that is 0.9999999999999999999999999999999999999999999c In this rocket we have a man in front of it and a man behind it. The front rocket man tells the back rocket man that he will stop the rocket speed impulsively (with infinite acceleration) when he passes planet mars by a certain amount of space so that the back of the rocket still is behind the marcian goal. What reality should the rear rocket side observe, one in which the front man is still in it's way to get at the red planet or the other, in which the front man has already passed the planet. I honestly think that the rear rocket man will travel in time to past and experiment a deja,vu. What do you think ?
I was really quite excited, as I had thought about this problem but never really bothered to find out... but then the answer is completely unimaginable and weirder than I imagined😊 Thanks for explaining and the great videos!
The first couple chapters of Brian Greene’s “The Elegant Universe” explain relativity and time dilation in layman’s terms which makes it pretty easy to understand.
Perception does not change reality, the train fits in the tunnel, therefore it does not get chopped. Taking into account for the distance from the guillotines an observer in the exact middle (and able to see both ends) would see the guillotines drop simultaneously. Observers on either side would see the guillotine closest to them drop first. There is no paradox.
Relativistic effects near or at the speed of light actually affect more than just your subjective perception. Physical distances/lengths ACTUALLY do contract or expand. Rate of time ACTUALLY DOES speed up or slow down. It's not just an "illusion." You're physically/chemically aging faster or slower down to every cell process and chemical process (yes, even the "speed of chemical reactions" goes up or down depending. You can't do that with just your perception, lol.) Yea, it's weird, but as far as we can tell, that's actually the strangeness of reality.
Question about the person on the train. Assume the person is looking forward. Will space-time be contracted in front of the person and would it be expanded behind him (kind of like the Doppler Effect?) That would explain why they would see the front guillotine go off first and the back one go off 2nd? i.e the observer is in the middle of the tunnel and has already passed the back guillotine but is moving towards the front guillotine. Love your all channels! Cheers!
It's been everywhere for decades if you just care to listen closely, lol. It's like a long running joke among sound editors to see if they can sneak it into every project they work on at least once in some tiny spot... or with some others, they try to see how many times they can use it in a single project and still get away with it ;)
What if you put a rigid bar between the guillotines with a lever in the middle mechanically attached to the guillotines which meant they had to close together? the bar would bend or snap in the case of one opening "before the other"...
There is and it is simple to think about. The train on a streight path compresses in direction x-y (front to back), when you add direction z (left or right) the train will be also travling in c (speedd of light) in z (left-right) direction, therefore compressing enough to clear the tunnel in z direction.
Please solve this relativistic paradox. It's not a textbook case, it's a case I thought of myself and I cannot find a solution. There are two asteroids with a small rest mass, one made out of matter and the other made out of antimatter, that are travelling at a constant relativistic speed toward a spaceship. However, they also have a small lateral velocity that will cause them to collide with each other and annihilate, just before colliding with the spaceship. From the point of view of an astronaut aboard the spaceship, the spaceship is at rest, while the two asteroids are approaching so fast that their mass is enormously increased. So much that the energy produced by their annihilation is exactly the amount that would be needed to melt the entire spaceship by mere heat radiation. However, from the point of view of the sentient space worm that dwells in one of the asteroids, the asteroids are actually at rest (except for the small lateral velocity that will eventually cause them to collide and annihilate), while it is the spaceship that is hurtling through space at a relativistic speed, and therefore has its mass enormously increased. Thus, the space worm concludes that the asteroids will annihilate, but the released energy will be various orders of magnitude smaller than what would be needed to melt the entire spaceship. Who is right: the astronaut, the space worm or none of the two? Will the annihilation completely melt the spaceship or not? Why?
I am by no means an expert but my initial thought is about the conservation of Energy. The total Energy is the same from both points of view, either it has enough to melt the ship or it doesn't. The relativistic increase in mass hasn't created new Energy.
funkyheadZOMG Remember that mass *is* energy. E=mc^2. Even if the total energy of the system is the same for both points of view, the two points of view do not agree about *where* that energy is.
Sorry didn't make myself clear (like I said; not an expert) I meant the total energy of each individual object is the same. It's true that mass can be converted into energy and visa-versa but the total energy of an object is not just it's mass. The relativistic increase in mass is due to the universal speed limit of light in a vacuum (c). The speed comes from the energy not the other way around. Apparently it's not an actual increase in mass in the classical sense. Anyway I too would like to read a more educated reply than mine.
I believe the astronaut would be correct here; the extra energy of the asteroids is due to their apparent velocity; when they annihilate, that excess energy will still be present in the blueshift of the photons approaching the astronaut. He will essentially see a brighter, more energetic explosion (at least towards him) that has the energy to do damage, while your space worms will see a rather normal explosion, but with an astronaut flying through at such high speeds that the extra force from hitting the blast radiation causes the extra damage. tl;dr, even though light travels at the same speed for all observers, it doesn't carry the same energy for all observers.
My guess is the spaceship won't get destroyed, and will see only a small amount of energy coming its way because i think that it's all dependent on the (small) rest mass of the asteroids.
So question, if instead of two guillotines, I had one guillotine that had two glades and were connected. From the perspective of the people on the train, would the part where the two guillotines are connected appear to bend?
***** Yes. When you drop an object, not every part of it falls simultaneously. The falling energy propagates as a wave through the object (look up some slow-mo vids of Slinkys being dropped and you'll see what I mean). So say you have a single H shaped blade that is held up by a claw in the center. When the claw releases it starts a "falling wave" beginning at the center of the H and spreading outward toward the blades. But to the people on the train, the blades are moving toward them, so from their perspective the blade on the far side is moving *toward* the source of the falling wave and so "catches up" with it very quickly and begins falling first, whereas the blade nearest them is moving *away* from the source of the wave and takes much longer to begin falling. Thus the H would seem to bend, and you'd end up with the same situation as shown in the video.
In the same vein as OP's question, what would happen if you used two lasers at either ends of the tunnel to detect when the train passes over them? And if you used lasers connected to the front and rear of the train, would this data be incongruent with the data obtained from the first set of lasers?
***** Yes, but my question is regarding the congruence between two methods of data aquisition. ie: lasers moving at near the speed of light, being detected by stationary detectors vs detectors moving at near the speed of light detecting stationary lasers. That was the point of my question - sorry for any confusion.
It is quite simple: When you are looking in front of you, pointing the tunnel, and you would look back, that image would be stretched almost to infinity (when looking in front of you would get squashed). Like we are watching the past at distant objects. So the train is fitting perfectly.
"have to move together". What you've just described is simultaneity, which, as the video explains, is relative! So the guillotines come down both at the same time, and also one after the other depending on the frame of reference.
Then you'd have to trust him not to lie, since everyone else (from their own reference frame) already thinks/has perceived that they are right as well, lol. Then, the ump could just lie about any call and people would just have to believe that's what he actually saw from his reference frame, even if that's not what he saw. At least in actual baseball in real life, you can review a play and disagree with the umpire. With relativistic baseball there'd never be an outside "objective" reference frame like a video recording that everyone could agree on. In real life there's at least more checks and balances that stop/discourage an umpire from being able to lie as freely as that without being able to be double-checked at all, lol.
Uneducated guess but from the perspective of the passenger, would the far end guillotine go first because from their perspective things in front of the train are squished and to the rear of the train are elongated? Thus time moving faster in front of the train amd slower behind?
For those of you who can't wrap their mind around the concept, take vision for example. Hold your finger a couple inches in front of your eye, then compare how large it seems compared to various items in the room. Is your finger really larger than your guitar? From your reference point it appears so, but from someone else in the room's ref point, the guitar is obviously bigger.
So, if everybody were blind, what happens then? Is this paradox stating that for the actual result being an unhurt train it is dependant on having onlookers and being empty? If the train and the tunnel were the exact same lenght, objectively there should be a short time window where the guillotine could come down and just scrape the paint of both ends of the train. This is what should happen if nobody around at all. It seems very far fetched to me, but are they then able to measure the actual distance the train shrinks relative to the lenght of the tunnel when viewed as a bystander? From the perspective of someone aboard the train (or the train itself) does this paradox state that it is absolutely impossible for the two guillotines to come down at exactly the same time? Or, I might have misunderstood, and it simply saying that the train WILL be stretched because it is moving while the tunnel is standing still. The train has its own "subjective perspective" so to speak, and it's not emphatically inclined and doesnt give a hoot about what any onlookers see. Therefor it can only have one outcome: the ends will be chopped off? I guess in the end what I am really wondering is: Is this theory relevant only for the phenomenon of perspective (subjective), or is it saying that perspective is relevant for the actual physical outcome? Edit: After some more research I understand that the closer to the speed of light the train moves, the shorter it becomes. It compresses. Also, the tunnel will be compressed from it's perspective. Wont these compressions cancel eachother out?
In that case, the train would smash into the one on the end. From the point of view outside train, it would smash after both closed. From the point of view inside train, it would smash, and afterwards the blade in the entry to the tunel would close after it. Or so I suppose, it at least looks consistent.
cm3007235 >The bystander would see the train smash into the front blade...< The train could not have smashed into the blade, or been observed to do so. It comes out intact. Viewing the incident under normal speeds, the train goes through the tunnel unharmed. Viewing the train now going at the speed of light, the train still comes out unharmed.
Agimaso Schandir I was talking about the case in which the blades come down but don't go back up. Are you saying that the train wouldn't crash into the blade after it has come down and stayed down?
Special relativity throws out the notion of simultaniety and creates the twin paradox. General relativity resolves the twin paradox and refines what "simultaneous" really means. Only the "observation" of simultaniety needs to be thrown out and NOT the notion of simultaniety itself. After all, quantum entanglement effects are said to happen instantaneously over any distance, even across the universe. So if two entangled particles on opposite ends of the galaxy changed their spin relative to each other and it happened "instantly"; did it not also happen simultaneously? We rely on "observation" to tell us when something happened. But observation depends on the speed of light. When we "see" something it is already in the past. It took a very tiny amount of time for light to get to our eyes. Nobody has ever seen anything at the time that it occurred. Observation also depends on how we measure our own time in our own reference frame.
You're absolutely right, so I'm not too sure what you're missing because you just explained what happens perfectly! When one reference frame sees two events as simultaneous, another reference frame will not, so long as the frames are moving relative to each other in a way that is not perpendicular to the line between the two events. Whether frame A or frame B sees them as simultaneous doesn't matter; the other frame will not.
+Greg Scott The Atlas of Creation was randomly sent to multiple scientists for free, with or without their consent, richard dawkins explains the matter; no one takes that abomination of a book seriously anyway.
+Chitranjan Baghi The train would stop when it hit the front gate, so its velocity would decrease. Now, the people outside the train no longer see its length contracted, and the people inside the train don't see the tunnel's length contracted, to yeah, everyone will just see the train crash into the front one, and the back one closing behind it.
I'm thinking that the signal propagation has something to do with it. In reality this would be more complicated because you need to trigger the guillotines and that takes some time (signal propagation is maybe 80% of the speed of light and the train is moving at maybe 99% the speed of light so none of this is negligible), and the guillotines also would have to move close to the speed of light so you'd have to account for that... it's not straightforward. Just earlier today, for comparison, I was thinking about how if you want to be precise about figuring out how far away a lightning strike was, you have to take both the speed of light and the speed of sound into account to your calculation, and I had to break out the pen and paper to figure it out. If something as simple as counting seconds between thunder and lightning isn't intuitive (if a is speed of sound, the distance to the lightning was delta_t *(ca)/(c-a)), the trains and guillotine experiment is surely much harder to figure out.
To the train-watching observer, it would appear that the back, then subsequently the front, of the train was cut off. The train being physically (well, relativistically) longer and having its ends chopped off simultaneously in the reference point of someone on the train is the same as a slightly compressed train pass through a longer distance, in which the guillotines do not appear to be simultaneous, to a stationary observer. To describe something as simultaneous only truly works for a given reference frame, as relativistic motion alters the order in which events are experienced relative to that observer, as the video points out. I suppose easiest way to describe it would be a sort of temporal doppler effect, if that makes any sense.
CrazyGrape"The train being physically (well, relativistically) longer and having its ends chopped off simultaneously in the reference point of someone on the train is the same as a slightly compressed train pass through a longer distance, in which the guillotines do not appear to be simultaneous" how is having the ends chopped of the same as the guillotines activating at different times (and the ends not being chopped off)?
If you are moving in the horizontal direction, then only the horizontal direction around you will be contracted. So if there were a thin copper wire hanging perpendicular to this line of sight (vertically) it won't look any different. It's time however still clicks slower
Time only stops relative to the photons of light moving at the speed of light, time still continues for an observer, thus the light still moves relative to the space around it over a time interval.
Super Hans From the perspective of an earthly observer, time seems to proceed normally and photons travelling from the sun cross 93,000,000 miles. From the perspective of the photons, time seems to proceed normally, but the distance in the direction of travel is compressed to zero. So, in a sense they don't move within their own reference frame. That's the best of my understanding.
I think of length contraction/time dilation as time skew. Different points in space in one reference frame correspond to different points in time in another. Because the train is traveling in the direction that time is skewed, making it seem shorter as the front car is further in the past, and hasn't gotten as far as the back end, which is in the future.
So you mean that the U-shape will physically be broken or the train will shrink ? I know that the shown test is about the perception. My point's a bit different, I know the answer. Just wanted to see how different people think :-)
Dennis Edlund even light from the sun took 8 minutes plus to reach the earth. when you imagine the train is travelling close to speed of light. the information from guillotine1 to guillotine2 will not exceed the speed of light. therefore the lag didn't against the laws of physics.
"Perspective" refers to the way shapes of things change with distance, It has nothing to do with relativistic distortion. Relativistic distortion is profound like time dilation. If you could actually measure the train from the other inertial frame it would be shorter no matter how you did it.
3:15 taking into account the delay it takes for light to reach "myons eyes", the myon would actully see the tree not as normal width but smaller of much radius (if it was travelling towards it) and not few millimiters tall but actually taller than stationary. This is because oncoming objects look longer than those moving away from us. This effect counteracts and dominates lenght contraction. Same with tunnel. It would not appear visully shorter from the trains perpective, actually it would look longer.
Depends upon the speed of the object in question. If you Google gamma factor and goto images, you'll be able to find a graph of the gamma factor graphed against the speed of light. You'll notice it starts off small and gets rather large as you approach the speed of light. If you had a gamma factor of 2 (corresponds to around 0.866c or so) your length would be half as long. So it is noticeable at large speeds definitely.
How Han Solo travelled less than 12 parsecs. From his PoV he compressed space to such a small distance he didnt have to travel that far. If someone knows the normal distance he should have travelled im sure someone out there can work out what fraction of the speed of light he was going at.
Unfortunatly, it is very unlikely for that to happen. Predictions made through theory in SR have been already observed and measured. This is the way our universe works, and it's not "madness".
So, assume the fellow pulling the guillotine lever has it hooked up to EM transmitters, and the guillotines themselves are tripped by identical EM receivers, and that the lever is exactly halfway between them both. Since c is c in every frame, and the distance between lever and blades are the same, why would one (the front) drop before the second (back), according to the train? What could the passengers point to to explain the delay in the second blade?
An easy way to show relativity is to get a measuring tape out and take a metre long piece of string. Obviously facing it straight on the string looks like 1 metre when measured, but then take a step to the left, and make sure you can still see the 0 touching the end of the string. Depending on which end your 0 is at, the string will be measured as longer or shorter than 1m, and if you stand the same distance in the other direction, the opposite will happen.
You would perceive the plane being contracted according to you. Everyone would agree that the passenger and you are furthest away from each other and that the pilot is in the middle. As for the distance from the observer to the plane, what point on the plane are you referring to? You would be furthest from the plane assuming that any point on the plane is considered equally close.
since the chip is either in the reference frame of the observer (installed in the tunnel) or in the reference frame of the passenger (on the train), it will produce different results. if it's in the tunnel the light will light up for both. if you put it on the train the light won't come up at all. it's not your perception that is affected by this it's everything. the chip will only receive the signals simultainiously if it's in the observers reference frame.
Not exactly. From an observer on the train the second guillotine still wont fall until the back of the train has entered the tunnel so the end result will be consistent. That is, it will appear as if the front of the train collided with the forward guillotine. And after collision, it wont be traveling as fast anymore so the length contraction effect will stop occurring and it will again fit snugly inside the tunnel.
Is the explanation for the difference in simultaneity, the fact that any observers inside the train would be traveling towards the front of the tunnel and away from the back? Meaning that the photons indicating that something has occurred in front of the train would be meeting the train halfway, while the photons indicating that something has occurred behind the train, would be racing to catch up to the observers, having to travel further?
But what if the blades of the guillotine weren't lifted so that the train would either crash into the second guillotine or be chopped? That way the train would either be totaled from the crash or totaled from being chopped, and simultaneity isn't a problem anymore. If the train is shorter than the tunnel, it crashes into the guillotine and if it is longer it gets chopped.
if you consider that in the reference frame of the person that the train is traveling relative to, the train gets smaller and from that of the person on the train the tunnel gets smaller so from the reference frame of someone analysing the experiment, both the tunnel and the train gets smaller but the rapport between their lengths stays the same. That to say if the guillotine was set to come down after the train went through the tunnel it would neither chop the tail nor the front of the train, since from the point of view of the guillotine's blades, the train gets smaller because it was moving relative to the blades.
well the guillotine on the right would come down in front of the train and the train would crash into it, but the shockwave from that collision can only travel as fast as the speed of light so by the time the crash effected the back end, it has already made it to the second guillotine, so that in turn comes down after the train has passed it. so pretty much the same as both events, but involving a crashed train. hope this helped
This thought experiment is an excellent example that illustrates the need to be careful when doing special relativity. The analysis from the point of view of the hill is easy, and it gives the correct result, but the issue of relativity of simultaneity makes the analysis from the train's point of view a bit more complicated. One can use the minkowski diagram to solve this problem.
Just a thought here: It's just like sound, that's due to the finite speed. If you change the guilliotines with sound systems, the guy watching will hear the sound of both at the same time, but the guy on the train will hear one and then the other.
I think once the train collides with the first guillotine the train is no longer moving and so the tunnel and the train are then in the same inertial frame. This means that in any frame the lengths of the train and the tunnel are the same and so when the second guillotine strikes nothing happens. So whichever reference frame you're in, you see the same thing.
i don't quite understand what you are implying. i would think matter affects time because time is based on matter and its movements/changes. matter seems to have a pull on space-time and we see evidence of those distortions everyday
The distortion of size occurs in the direction of movement, so it will change over time. Each cart will see itself approaching a tunnel too narrow for it, but then changing shape to fit around them. I think.
Try thinking about this if you were to put in a small neutron star or BH along with its time dilation effects, then note if its extreme enough you could actually walk to the other side to let a longer object out.Works into a really good theory to explain how the universe started but its too much for here.Its postulate is that time dilated contraction of matter is indistinguishable from space expansion and shows a testable way of showing that space expands around any gravitational object.
In the concept of relativity of simultaneity, why must the gillotine in the front of the tunnel is dropped and raised before the gillotine in the rear of the tunnel is dropped and raised? Also doesn't this mean that length contraction is only an apparent effect since the train comes out of the tunnel unharmed?
Another question, relating Lorentz contraction: If you see distances squashed in a certain direction when travelling at relativistic speeds, then aren't you able to figure out your absolute movement (as if the universe had an actual absolute axis of reference) by noticing that the atoms are much closer together in a certain direction than in others?
How long do objects appear in the opposite direction of the motion? Do they get longer? If the contraction occurs only in the direction of movement, then the Trainspotter had to be standing by the rightmost exit of the tunnel, as the train was rushing towards him, not away from him. Then when he pushed a button to activate the guillotines, the further one on the left did in fact come down later because of the delay on the cable.
Objects travelling near or at the speed of light warp local space. So yes, what you're saying really does happen. Why do you have a problem with this? Warping space =/= warping the material the train is made out of.
The tunnel and the train are the same size no matter the speed of the train. The train may grow slightly from friction and the heat causing the metal to expand. The shock wave created in front of the train may decimate the tunnel at high enough speeds, but nothing changes the size of either object. The guillotines are the key to making this work. If the train were moving 1 cm per year along the track, it would be easy to get to a point where the guillotines could close, enclosing the train and open in time to let the train out. However, the faster the train goes, the more difficult it becomes to close and reopen the guillotine in time due to the mass of the guillotines. The energy required to move the guillotines down and up in a fraction of a second is enormous, plus, the materials that make up the guillotine might not be strong enough to withstand the forces needed to move them that quickly.
If you move at constant velocity = v, then it would shrink ,x=x'√(1-v^2/c^2 ) x is the distance when moving, and x' is the distance when the object is not moving.
It would matter where the person on the train was sitting. If he was in the middle, perhaps the tunnel in front would appear compressed, but then the rear of the tunnel would have to be stretched. So when he is half way through (or less) he pulls the blades down becausu there is more room to the back of the tunnel
A lot of people here are asking what if blades never go up. And they get "train crashes int second blade" as an answer. While the real question is "Suppose train is actually longer that tunnel, and get shrinked, fits into tunnel and crashes into second blade, what happens next, assuming the blades are infinitely more sturdy than the train?" From outside point of view, the whole train went inside tunnel, then crashed. How come it's still inside the tunnel, between closed blades, distance shorter than length of the train? From train's point of view, moving tunnel gets even shorter. The head of the train reaches exit and suddenly crashes into second blade while the tail is still outside of tunnel. Shouldn't then the tail stop and be cut off by the first blade? The answer is, signals propagate with finite speed of light, thus by the time signal about crash (either warning message or wave of structural damage) reaches the end of the train, it will already be inside the tunnel.
The back gets chopped off in neither. From the perspective of the person on the train, the train will smash into the first guillotine that comes down; the one at the end of the tunnel. Now that it has crashed into the guillotine it is no longer moving, meaning the tunnel is no longer compressed. As the tunnel is no longer compressed, due it being stationary fro the train's frame of reference, the second guillotine will fall harmlessly.
No one said time is a measure. "Time" is part of space-time, and has nothing to do with assigning values to intervals between events. That might be how we perceive time, but time is itself a dimension of space-time that has to do with causality; it determines that the "past" is the set of events that can send information elsewhere, while the "future" is the set of events to which information can be sent. An inadequate explanation, tbh, but hopefully sufficient.
In fact, the main lesson of relativity is that all reference frames are equally valid. There is no "correct" reference frame. The equations of Einstein's relativity allow one observer to determine what another observer will observe. Like the professor said, there is no "fact of the matter." One person sees this, another sees that, and they are both right as long as their observations are related by relativity.
This is not about having imprecise measurements. Even with perfect measurements the disagreement about what happens still exists. It´s not just like a lens distorting our view of the world. In relativity, the world actually does get distorted.
In order for the left cleaver to "trigger" the right cleaver, it would have to send a signal that could travel no faster than the speed of light. But the front of the train would reach the right end of the tunnel before any lightspeed signal could travel from the left end to the right end triggered by the back end of the train entering the tunnel, so the front would get chopped from both points of view.
I may be wrong, but I believe that the train observer will see the signals moving from each guillotine at different speeds, such that they will arrive at chip at the same time. The important thing here is not the timing of the switches, but the timing of the signal arriving at the chip. However, both will agree that there was a light.
My guess is that the train collides with the front guillotine and stops. No more contraction of the tunnel because it's not moving, so it's the same length as the tunnel and can fit inside. So when the back guillotine comes down it misses the back end of the train.
just a minor correction: the wave produced by the impact would not travel at the speed of light it would travel at the speed of sound. The train would be long gone by the time the back end felt the crash.
The way I see it: If the train is moving near light speed, then to an observer on the train after the observer passes through the tunnel entrance the portion of the tunnel between the observer and the entrance would stretch. So at the moment the front of the train is near the tunnel exit the tunnel has elongated to encompass the whole train.
Follow up question for the Professor: What if one of the guillotines is the cause for the other to fall ? Shouldn't they then fall in the same order for all observers independently of the frame of reference?
It's the same problem, when the guillotines come down simultaneously in one reference frame, the other frame will have the from one come down, and the back one will come down when the train crashes into the front one, slightly later
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This dude should be a rapper. He got mad scientific flows
"But I'm not a rapper."
So, to a proton speeding through CERN, the tunnel seems the size of a donut? mmm...donuts
moldycheesedisease calling Pogo....
I noticed too. You may call this respected scientist a science rapper. He really speaks fast with clear accent. Fantastic.
500
I've never watched, read, heard someone explain this paradox better than this.
Zero Cool Just on RUclips. And that one dude from Minnesota.
That guy is crazy
@@oatlord He's probably taught it a bunch of times. I know both of those paradoxes were both in my Modern Physics textbook in the end of the 1st or 2nd chapter. I'm guessing they're pretty common for textbooks. Mine had quite a few. I also remember one with someone running at relative speeds with a ladder towards a shed that is too small to contain the ladder XD It's similar to the train one.
@@oatlord Oh, and they also like to include one with twins and one gets sent off a near the speed of light to a distant star systems and then turns around and comes back. The cool part is where they send happy birthday messages to each other and how sometimes they seem too slow and sometimes they seem too fast between birthdays :P
I remember this question being in a physics exam I did 5 years ago. I answered it differently... but I still think it holds merit (I did well in the exam but no idea if I got this bit right - maybe someone can tell me?)...
So from the point of view of the train driver at the front of the train:
- when he is midway through the tunnel, he sees the tunnel in front of him Lorentz contracted, but behind him the other half of the tunnel is lengthened
- he still sees the guillotine miss both ends of his train because for him, the guillotine comes down when he is very close to the exit
Science Fact is stranger than science fiction.
+Geekage Science fiction has to make some sort of sense to us. Reality doesn't :)
+SarthorS
nice reply - sums it up well.
same thing
Fiction is limited by the imagination of men. Reality is way more creative than our brightest minds.
Science science is stranger than fact fiction.
I love the Wilhelm Screams when the blades chop off the train
This may be my favorite Sixty Symbols video. This guy explains things really well.
I still don't understand what decides that the other guillotine comes down first. Mind-blowing indeed.
I guess I should ask this: what if there were two tracks and two trains going in opposite directions, and they were inside the tunnel at the same time? Would they have contradictory opinions about which guillotine came down first?
The first one coming down first is because if you are moving towards the guillotine, the light from guillotine hits you first, so you think that event occurred first.
To answer your second question with 2 sets of tracks, yes, people on different trains will have a contradictory outlook on what occurred first
niko that just raises a new question, why the 2nd guillotine's light seems to come 1st
Playitalready because of the direction of travel.
its traveling towards both sides 1 by 1
what do you mean "1 by 1"?
What'd happen if you were to place a very long surface (like a long wooden plank or something) resting on the top of both guillotines with a bowl with any liquid; in such a manner that, if the guillotines are not both at the same height at the same time, the plank won't be leveled and the water will spill.
From one perspective the water wouldn't spill because both blades fall and rise at the same time without chopping the train off. But from the other perspective the water would spill because they don't fall at the same time; and quoting from 5:22 that's something that has to be agreed upon because either the water gets spilled or it doesn't, since it's not a matter of perspective.
but the information cannot exceed C, the plank cannot bend faster than the speed of light
Not an expert but guessing the plank would appear to bend from perspective of train
Hey you still alive
the plank breaks. This is essentially another famous paradox, and that's the resolution.
I really like the way that he explain things, and Brady's interactions as well
Pops into existence to see the Earth rushing up to meet it?... Kind of sounds like a whale to me.
Oh dear. Not again
This made me chuckle. Well played, sir
strange, makes me think about pots of petunias...
+max norman pots of petunias? Sounds familiar for some reason, as if I've heard of it before...
Infinite Improbability drive, Hitchhiker's Guide to the Galaxy
Could we get a Numberphile video or something that focuses on the maths behind this? I'd quite like to hear more about that, because if it's as simple as Prof. Merrifield here makes it sound, I might be able to figure it out myself.
I love this analogy. I have had a hard time explaining this to other people. Well done.
The last 5 seconds of the video... I have my headphones on full volume, I go to put my laptop down, and I think the video is over... and all of a sudden I hear a guillotine snap down hard. That scared me out of my mind.
really enjoyed this - the guy in the video explained it so well that i think i actually understood it!
The math, as they say in the video, really is relatively simple. If you want a complete understanding of the topic, I highly recommend googling it. If you have any questions, try reddit or stackexchange.
+Alex I
Yep, very simple math. Trigonometry. I can't even pass Algebra for crying out loud. And is sad because I really love physics but my brain cannot do math properly.
+Bassotronics I'm exactly like you I love listening to university courses, listen to books, I love it but not smart enough to understand a lot of it, there's one video with mark leweldin not exactly the way it's spelt, but you should watch it it's on RUclips, it's his last university course, it is awesome.
Dylan Parker You think, my friend, you think.
I thought I understood it too, so I must be missing something
This was probably the best explanation to this problem I have seen. I never quite understood it intuitively before. Thanks!
I'd love a response to this from someone on or behind the camera. Couldn't think of a particular video where this comment would've been more 'correct', I like this channel. Anyway, I was an IT instructor for quite awhile, could easily still stand up in front and do some teaching. Here's the ONE THING I always thought would give the 'rubber sheet' gravity graphic greater value as a visual aid. Draw AT LEAST TWO rubber sheets, offset from one another, specifically to 'break' the mind's capability of abstraction of the habit of thinking in only three dimensions. Since every graphic of the solar system ever drawn appears as an extended elliptic ("The axis of rotation is NOT perpendicular to the plane of the ecliptic."), people tend to incorporate that little bit of trivia into their 'new understanding' of how gravity works, once they've finally seen the 'rubber sheet' graphic. But the 'single rubber sheet' fails to specifically illustrate that the curvature of spacetime around a massive object, (BTW, the spell checker shouldn't redline the word "spacetime", Google. Shame on you!), it fails to specifically illustrate that the curvature of spacetime around a massive object is totally xyz-coordinate-independent. It curves in all possible directions, related best to some gravity-influenced object by showing that it is vector(?) dependent. Whichever direction the approaching (or orbiting) object is in relation to the other object, THAT will affect what vector(?) the two bodies will respond to each other 'in'. I think this would be MUCH better illustrated by including at least TWO exemplar 'rubber sheets' in every graphic depiction of same. Just my opinion. Would love to hear the Professor's opinion. Please forgive the probable misuse of the term "vector", although I'm pretty sure you know what I mean to say.
Show us the maths pleeeeeease!
681726 it's very easy to find but difficult to understand. Lorentz transformations should get you on the right track
My mind is bending. But only as seen on the inside.
Underrated
If I ask, then, "what really, exactly, absolutely happened?" the answer would be, "it depends on the reference frame" ?
So it's like saying that reality is relative?
Leif Urdaneta Not really. Reality isn't relative, but our *perception* of it is. The question of what "absolutely happened" makes no sense, because we're only talking about how people moving at different velocities perceive spacetime from different perspectives. In the example of the train, separate inertial observers will disagree on the time the blades dropped, the length of the tunnel vs. the train, and the masses of the tunnel and the train - but they will always agree that the train passed through the tunnel unharmed.
Let's say I draw a chalk circle on the wall in front of me. I ask you, "Do you like my circle?" But you're standing a few feet to my left and viewing it at an angle, so you say "It's not a circle, it's an ellipse!" Then our friend leaning against the wall says "It's not a circle *or* an ellipse. It's just a line!" All of our perceptions are "correct" - there's nothing special about my perpendicular angle that makes a circle the "right" way to see it - we're just seeing the same thing from different perspectives. And at the same time, our different perceptions don't change any facts about reality - no matter what angle you're looking from you'll never see the circle as, say, a square or a triangle.
That's essentially what's going on in special relativity. Changing your velocity changes your perception of time, distance, and mass by changing your perspective in spacetime, but it doesn't change spacetime itself.
Exactly. To the observer near the tunnel the train would stretch out as it decelerated. And for the people on the train, they would stay the same while the tunnel and the rest of the outside world stretched out.
Oners82
I guess it depends on how you define "reality," but imo, "reality is relative" is a bad conclusion to draw from SR.
Like I said before, in the train example there is no observer that will see the train get cut in half while another sees it safely travel on. The overall outcome of any situation will remain the same for all observers. "Reality" is preserved in that sense and is certainly *not* relative. Otherwise, we'd have paradoxes coming out of the woodwork.
All that's relative is time, distance, and mass, which warp depending on your velocity. Those are "real" effects in the sense that you can measure them, but you can measure the warping of regular 2-D perspective too. And even though, say, a ruler looks shorter when I view it at an angle, we never say the ruler *is* shorter when I view it at an angle. We understand that it's an issue of perception due to my relative position to the ruler. SR is a little more far-reaching in its claims, but it's essentially the same thing. And I think it's easier to understand that way.
I think you're just not listening to what I'm saying. Which I don't blame you, considering these are RUclips comments, but the question was "Is reality relative?" And I say no, it isn't. Despite the fact that two observers in different inertial frames disagree on the simultaneity of events and the lengths/masses of objects, they must agree on *everything* else, and even their disagreements must be symmetrical. I'm not saying the effects of SR are just illusions, or that there is any "correct" reference frame. I'm saying that all observers experience the same "reality," just warped and skewed based on their relative velocities. It's more of a philosophical point now that I think about it, but I still think it's an important distinction.
RoboBoddicker
So just imagine this one:
I'm going from earth to mars with a rocket. But I'm going at a speed that is 0.9999999999999999999999999999999999999999999c
In this rocket we have a man in front of it and a man behind it.
The front rocket man tells the back rocket man that he will stop the rocket speed impulsively (with infinite acceleration) when he passes planet mars by a certain amount of space so that the back of the rocket still is behind the marcian goal.
What reality should the rear rocket side observe, one in which the front man is still in it's way to get at the red planet or the other, in which the front man has already passed the planet.
I honestly think that the rear rocket man will travel in time to past and experiment a deja,vu.
What do you think ?
I was really quite excited, as I had thought about this problem but never really bothered to find out... but then the answer is completely unimaginable and weirder than I imagined😊 Thanks for explaining and the great videos!
The first couple chapters of Brian Greene’s “The Elegant Universe” explain relativity and time dilation in layman’s terms which makes it pretty easy to understand.
Perception does not change reality, the train fits in the tunnel, therefore it does not get chopped. Taking into account for the distance from the guillotines an observer in the exact middle (and able to see both ends) would see the guillotines drop simultaneously. Observers on either side would see the guillotine closest to them drop first. There is no paradox.
Relativistic effects near or at the speed of light actually affect more than just your subjective perception. Physical distances/lengths ACTUALLY do contract or expand. Rate of time ACTUALLY DOES speed up or slow down. It's not just an "illusion." You're physically/chemically aging faster or slower down to every cell process and chemical process (yes, even the "speed of chemical reactions" goes up or down depending. You can't do that with just your perception, lol.) Yea, it's weird, but as far as we can tell, that's actually the strangeness of reality.
Question about the person on the train. Assume the person is looking forward. Will space-time be contracted in front of the person and would it be expanded behind him (kind of like the Doppler Effect?) That would explain why they would see the front guillotine go off first and the back one go off 2nd? i.e the observer is in the middle of the tunnel and has already passed the back guillotine but is moving towards the front guillotine. Love your all channels! Cheers!
Ever since I've played SW Battlefront this freaking Wilhelm-scream is EVERYWHERE...
+Peter Timowreef AGH!
+Peter Timowreef I'm surprised you haven't tired sooner, pretty much every hollywood/bandwagon-movie has it.
Benjamin Antman
I don't watch an awful lot of hollywood.
or ever since every movie since i was born.
It's been everywhere for decades if you just care to listen closely, lol. It's like a long running joke among sound editors to see if they can sneak it into every project they work on at least once in some tiny spot... or with some others, they try to see how many times they can use it in a single project and still get away with it ;)
What if you put a rigid bar between the guillotines with a lever in the middle mechanically attached to the guillotines which meant they had to close together? the bar would bend or snap in the case of one opening "before the other"...
There is and it is simple to think about. The train on a streight path compresses in direction x-y (front to back), when you add direction z (left or right) the train will be also travling in c (speedd of light) in z (left-right) direction, therefore compressing enough to clear the tunnel in z direction.
7:41 amazing flow! mike eminem merrifield!
Please solve this relativistic paradox. It's not a textbook case, it's a case I thought of myself and I cannot find a solution.
There are two asteroids with a small rest mass, one made out of matter and the other made out of antimatter, that are travelling at a constant relativistic speed toward a spaceship. However, they also have a small lateral velocity that will cause them to collide with each other and annihilate, just before colliding with the spaceship.
From the point of view of an astronaut aboard the spaceship, the spaceship is at rest, while the two asteroids are approaching so fast that their mass is enormously increased. So much that the energy produced by their annihilation is exactly the amount that would be needed to melt the entire spaceship by mere heat radiation.
However, from the point of view of the sentient space worm that dwells in one of the asteroids, the asteroids are actually at rest (except for the small lateral velocity that will eventually cause them to collide and annihilate), while it is the spaceship that is hurtling through space at a relativistic speed, and therefore has its mass enormously increased. Thus, the space worm concludes that the asteroids will annihilate, but the released energy will be various orders of magnitude smaller than what would be needed to melt the entire spaceship.
Who is right: the astronaut, the space worm or none of the two? Will the annihilation completely melt the spaceship or not? Why?
I am by no means an expert but my initial thought is about the conservation of Energy. The total Energy is the same from both points of view, either it has enough to melt the ship or it doesn't. The relativistic increase in mass hasn't created new Energy.
funkyheadZOMG
Remember that mass *is* energy. E=mc^2. Even if the total energy of the system is the same for both points of view, the two points of view do not agree about *where* that energy is.
Sorry didn't make myself clear (like I said; not an expert) I meant the total energy of each individual object is the same. It's true that mass can be converted into energy and visa-versa but the total energy of an object is not just it's mass. The relativistic increase in mass is due to the universal speed limit of light in a vacuum (c). The speed comes from the energy not the other way around. Apparently it's not an actual increase in mass in the classical sense. Anyway I too would like to read a more educated reply than mine.
I believe the astronaut would be correct here; the extra energy of the asteroids is due to their apparent velocity; when they annihilate, that excess energy will still be present in the blueshift of the photons approaching the astronaut. He will essentially see a brighter, more energetic explosion (at least towards him) that has the energy to do damage, while your space worms will see a rather normal explosion, but with an astronaut flying through at such high speeds that the extra force from hitting the blast radiation causes the extra damage.
tl;dr, even though light travels at the same speed for all observers, it doesn't carry the same energy for all observers.
My guess is the spaceship won't get destroyed, and will see only a small amount of energy coming its way because i think that it's all dependent on the (small) rest mass of the asteroids.
So question, if instead of two guillotines, I had one guillotine that had two glades and were connected. From the perspective of the people on the train, would the part where the two guillotines are connected appear to bend?
***** I believe the connection would appear to contract in front of them and stretch out behind them.
***** Yes. When you drop an object, not every part of it falls simultaneously. The falling energy propagates as a wave through the object (look up some slow-mo vids of Slinkys being dropped and you'll see what I mean).
So say you have a single H shaped blade that is held up by a claw in the center. When the claw releases it starts a "falling wave" beginning at the center of the H and spreading outward toward the blades. But to the people on the train, the blades are moving toward them, so from their perspective the blade on the far side is moving *toward* the source of the falling wave and so "catches up" with it very quickly and begins falling first, whereas the blade nearest them is moving *away* from the source of the wave and takes much longer to begin falling. Thus the H would seem to bend, and you'd end up with the same situation as shown in the video.
Logan Poppe What you said was contradictory. If the connection contracts, gets shorter, it wouldn't stretch out behind them.
In the same vein as OP's question, what would happen if you used two lasers at either ends of the tunnel to detect when the train passes over them?
And if you used lasers connected to the front and rear of the train, would this data be incongruent with the data obtained from the first set of lasers?
*****
Yes, but my question is regarding the congruence between two methods of data aquisition.
ie: lasers moving at near the speed of light, being detected by stationary detectors vs detectors moving at near the speed of light detecting stationary lasers.
That was the point of my question - sorry for any confusion.
It is quite simple:
When you are looking in front of you, pointing the tunnel, and you would look back, that image would be stretched almost to infinity (when looking in front of you would get squashed). Like we are watching the past at distant objects.
So the train is fitting perfectly.
"have to move together". What you've just described is simultaneity, which, as the video explains, is relative! So the guillotines come down both at the same time, and also one after the other depending on the frame of reference.
and what if the doors are quantum entangled?
This is one of the reasons why quantum mechanics doesn't like theory of relativity hahahaha
Wouldn't make a difference
Sheeeeet
Then when one is closed the other is open and vice-versa
my best guess is to say the mechanisms to close the doors use electricity, therefore, relativity holds....somehow??? I wish I understood tensors.
I would not envy the umpires in relativistic baseball...SAFE! Wait no! Ummm.
Can't you just use the judge's reference frame to make all those decisions?
the players would disagree and everyone would be right !! chaos
Then you'd have to trust him not to lie, since everyone else (from their own reference frame) already thinks/has perceived that they are right as well, lol. Then, the ump could just lie about any call and people would just have to believe that's what he actually saw from his reference frame, even if that's not what he saw. At least in actual baseball in real life, you can review a play and disagree with the umpire. With relativistic baseball there'd never be an outside "objective" reference frame like a video recording that everyone could agree on. In real life there's at least more checks and balances that stop/discourage an umpire from being able to lie as freely as that without being able to be double-checked at all, lol.
What of the guillotines stayed down once they had fallen?
Uneducated guess but from the perspective of the passenger, would the far end guillotine go first because from their perspective things in front of the train are squished and to the rear of the train are elongated? Thus time moving faster in front of the train amd slower behind?
For those of you who can't wrap their mind around the concept, take vision for example. Hold your finger a couple inches in front of your eye, then compare how large it seems compared to various items in the room. Is your finger really larger than your guitar? From your reference point it appears so, but from someone else in the room's ref point, the guitar is obviously bigger.
So, if everybody were blind, what happens then? Is this paradox stating that for the actual result being an unhurt train it is dependant on having onlookers and being empty?
If the train and the tunnel were the exact same lenght, objectively there should be a short time window where the guillotine could come down and just scrape the paint of both ends of the train. This is what should happen if nobody around at all.
It seems very far fetched to me, but are they then able to measure the actual distance the train shrinks relative to the lenght of the tunnel when viewed as a bystander? From the perspective of someone aboard the train (or the train itself) does this paradox state that it is absolutely impossible for the two guillotines to come down at exactly the same time?
Or, I might have misunderstood, and it simply saying that the train WILL be stretched because it is moving while the tunnel is standing still. The train has its own "subjective perspective" so to speak, and it's not emphatically inclined and doesnt give a hoot about what any onlookers see. Therefor it can only have one outcome: the ends will be chopped off?
I guess in the end what I am really wondering is: Is this theory relevant only for the phenomenon of perspective (subjective), or is it saying that perspective is relevant for the actual physical outcome?
Edit: After some more research I understand that the closer to the speed of light the train moves, the shorter it becomes. It compresses. Also, the tunnel will be compressed from it's perspective. Wont these compressions cancel eachother out?
What if the blades didn't come back up? They just fell and stayed down?
In that case, the train would smash into the one on the end. From the point of view outside train, it would smash after both closed. From the point of view inside train, it would smash, and afterwards the blade in the entry to the tunel would close after it. Or so I suppose, it at least looks consistent.
Then you go around the hill on the just-in-case-the-blades-don't-come-"back-up" [pun alert] tracks :p
cm3007235
>The bystander would see the train smash into the front blade...<
The train could not have smashed into the blade, or been observed to do so. It comes out intact.
Viewing the incident under normal speeds, the train goes through the tunnel unharmed. Viewing the train now going at the speed of light, the train still comes out unharmed.
Agimaso Schandir I was talking about the case in which the blades come down but don't go back up. Are you saying that the train wouldn't crash into the blade after it has come down and stayed down?
cm3007235
No. Did not realize that.
What would be the point of the blades staying down?
i like how he is incredibly similar to the 10th doctor in the way he talks.
Special relativity throws out the notion of simultaniety and creates the twin paradox.
General relativity resolves the twin paradox and refines what "simultaneous" really means.
Only the "observation" of simultaniety needs to be thrown out and NOT the notion of simultaniety itself. After all, quantum entanglement effects are said to happen instantaneously over any distance, even across the universe. So if two entangled particles on opposite ends of the galaxy changed their spin relative to each other and it happened "instantly"; did it not also happen simultaneously? We rely on "observation" to tell us when something happened. But observation depends on the speed of light. When we "see" something it is already in the past. It took a very tiny amount of time for light to get to our eyes. Nobody has ever seen anything at the time that it occurred. Observation also depends on how we measure our own time in our own reference frame.
You're absolutely right, so I'm not too sure what you're missing because you just explained what happens perfectly! When one reference frame sees two events as simultaneous, another reference frame will not, so long as the frames are moving relative to each other in a way that is not perpendicular to the line between the two events. Whether frame A or frame B sees them as simultaneous doesn't matter; the other frame will not.
Not really related, but I'm very curious about Prof Merrifield's interest in the "Atlas of Creation" he has on his shelf.
Thanks, Ole.
+Greg Scott The Atlas of Creation was randomly sent to multiple scientists for free, with or without their consent, richard dawkins explains the matter; no one takes that abomination of a book seriously anyway.
That helps. I've never seen it, but I understand the photography is very well done.
Sixty Symbols what if those gates doesn't go up back, what will happen then?
+Chitranjan Baghi everyone will just see the train crash into the front one...
+Chitranjan Baghi The train would stop when it hit the front gate, so its velocity would decrease. Now, the people outside the train no longer see its length contracted, and the people inside the train don't see the tunnel's length contracted, to yeah, everyone will just see the train crash into the front one, and the back one closing behind it.
But what happens if a guy inside train pulls the trigger for the guillotine?
Then the universe explodes.
I'm thinking that the signal propagation has something to do with it. In reality this would be more complicated because you need to trigger the guillotines and that takes some time (signal propagation is maybe 80% of the speed of light and the train is moving at maybe 99% the speed of light so none of this is negligible), and the guillotines also would have to move close to the speed of light so you'd have to account for that... it's not straightforward. Just earlier today, for comparison, I was thinking about how if you want to be precise about figuring out how far away a lightning strike was, you have to take both the speed of light and the speed of sound into account to your calculation, and I had to break out the pen and paper to figure it out. If something as simple as counting seconds between thunder and lightning isn't intuitive (if a is speed of sound, the distance to the lightning was delta_t *(ca)/(c-a)), the trains and guillotine experiment is surely much harder to figure out.
To the train-watching observer, it would appear that the back, then subsequently the front, of the train was cut off. The train being physically (well, relativistically) longer and having its ends chopped off simultaneously in the reference point of someone on the train is the same as a slightly compressed train pass through a longer distance, in which the guillotines do not appear to be simultaneous, to a stationary observer.
To describe something as simultaneous only truly works for a given reference frame, as relativistic motion alters the order in which events are experienced relative to that observer, as the video points out. I suppose easiest way to describe it would be a sort of temporal doppler effect, if that makes any sense.
+CrazyGrape Man, my grammar needs work...
CrazyGrape"The train being physically (well, relativistically) longer and having its ends chopped off simultaneously in the reference point of someone on the train is the same as a slightly compressed train pass through a longer distance, in which the guillotines do not appear to be simultaneous"
how is having the ends chopped of the same as the guillotines activating at different times (and the ends not being chopped off)?
If you are moving in the horizontal direction, then only the horizontal direction around you will be contracted. So if there were a thin copper wire hanging perpendicular to this line of sight (vertically) it won't look any different. It's time however still clicks slower
But what if the blades are connected with a steel rod at the top so that they have too come down at the same time?
What if the blade is a solid ring around the Mt. Special relativity is bull.
No, but it is relatively complex.
Pun intended.
+Guitar Dude no
it will simply look to be moving at an angle to people at the train
I am very very sad that you don't do the math in these marvelous videos.
If time stops at the speed of light then how does light move?
Somebody please explain this.
Time only stops relative to the photons of light moving at the speed of light, time still continues for an observer, thus the light still moves relative to the space around it over a time interval.
Yeah so if you're a photon travelling at the speed of light, then you don't move anywhere, cause time stops?
Super Hans From the perspective of an earthly observer, time seems to proceed normally and photons travelling from the sun cross 93,000,000 miles. From the perspective of the photons, time seems to proceed normally, but the distance in the direction of travel is compressed to zero. So, in a sense they don't move within their own reference frame. That's the best of my understanding.
Super Hans I think you would probly still be travelling through "space" but not through "time" i dunno, just a suggestion.
Super Hans
If there's a photon traveling at c, then it never sees you move, and the universe lasts forever inside the photon's reference frame.
I think of length contraction/time dilation as time skew. Different points in space in one reference frame correspond to different points in time in another. Because the train is traveling in the direction that time is skewed, making it seem shorter as the front car is further in the past, and hasn't gotten as far as the back end, which is in the future.
The use of The Wilhelm Scream in the animations was inspired!
Nice Willem screams.
Willem Dafoe?
No, the most famous scream in cinematic history. There are YT videos about it.
What happens if the guillotine are connected to each other as an U upside down.
Dennis Edlund I think they will see blade at fount come down first, then the blade at the back come down after
Dennis Edlund The U-shape changes as the train passes by.
So you mean that the U-shape will physically be broken or the train will shrink ?
I know that the shown test is about the perception.
My point's a bit different, I know the answer.
Just wanted to see how different people think :-)
Dennis Edlund even light from the sun took 8 minutes plus to reach the earth. when you imagine the train is travelling close to speed of light. the information from guillotine1 to guillotine2 will not exceed the speed of light. therefore the lag didn't against the laws of physics.
Nice explaination
Yay! who else nodded in appreciation upon hearing the Wilhelm scream?
"Perspective" refers to the way shapes of things change with distance, It has nothing to do with relativistic distortion. Relativistic distortion is profound like time dilation. If you could actually measure the train from the other inertial frame it would be shorter no matter how you did it.
3:15 taking into account the delay it takes for light to reach "myons eyes", the myon would actully see the tree not as normal width but smaller of much radius (if it was travelling towards it) and not few millimiters tall but actually taller than stationary. This is because oncoming objects look longer than those moving away from us. This effect counteracts and dominates lenght contraction.
Same with tunnel. It would not appear visully shorter from the trains perpective, actually it would look longer.
5:24 "My leg!"
Im so drunk and this is magic
WUT.
Depends upon the speed of the object in question. If you Google gamma factor and goto images, you'll be able to find a graph of the gamma factor graphed against the speed of light. You'll notice it starts off small and gets rather large as you approach the speed of light. If you had a gamma factor of 2 (corresponds to around 0.866c or so) your length would be half as long. So it is noticeable at large speeds definitely.
How Han Solo travelled less than 12 parsecs. From his PoV he compressed space to such a small distance he didnt have to travel that far. If someone knows the normal distance he should have travelled im sure someone out there can work out what fraction of the speed of light he was going at.
what if the guillotines stayed close and didn't open back
Once you hear the Wilhelm Scream, you hear it all over the place.
One day, we will look back and realise this was madness! The truth is yet to be found.
So what's your point? It's a theory. Theories change as new info is available.
+Luis Fernando Neves I wouldn't call it madness lol
+Luis Fernando Neves time contraction and space dilation can and have been tested/measured
Depopulation Agenda
"The truth is already on the internet"
Ok. So is creationism. What's your point mate?
Unfortunatly, it is very unlikely for that to happen. Predictions made through theory in SR have been already observed and measured. This is the way our universe works, and it's not "madness".
So, assume the fellow pulling the guillotine lever has it hooked up to EM transmitters, and the guillotines themselves are tripped by identical EM receivers, and that the lever is exactly halfway between them both.
Since c is c in every frame, and the distance between lever and blades are the same, why would one (the front) drop before the second (back), according to the train? What could the passengers point to to explain the delay in the second blade?
An easy way to show relativity is to get a measuring tape out and take a metre long piece of string. Obviously facing it straight on the string looks like 1 metre when measured, but then take a step to the left, and make sure you can still see the 0 touching the end of the string. Depending on which end your 0 is at, the string will be measured as longer or shorter than 1m, and if you stand the same distance in the other direction, the opposite will happen.
You would perceive the plane being contracted according to you. Everyone would agree that the passenger and you are furthest away from each other and that the pilot is in the middle. As for the distance from the observer to the plane, what point on the plane are you referring to? You would be furthest from the plane assuming that any point on the plane is considered equally close.
since the chip is either in the reference frame of the observer (installed in the tunnel) or in the reference frame of the passenger (on the train), it will produce different results. if it's in the tunnel the light will light up for both. if you put it on the train the light won't come up at all. it's not your perception that is affected by this it's everything. the chip will only receive the signals simultainiously if it's in the observers reference frame.
Not exactly. From an observer on the train the second guillotine still wont fall until the back of the train has entered the tunnel so the end result will be consistent. That is, it will appear as if the front of the train collided with the forward guillotine. And after collision, it wont be traveling as fast anymore so the length contraction effect will stop occurring and it will again fit snugly inside the tunnel.
Is the explanation for the difference in simultaneity, the fact that any observers inside the train would be traveling towards the front of the tunnel and away from the back?
Meaning that the photons indicating that something has occurred in front of the train would be meeting the train halfway, while the photons indicating that something has occurred behind the train, would be racing to catch up to the observers, having to travel further?
But what if the blades of the guillotine weren't lifted so that the train would either crash into the second guillotine or be chopped? That way the train would either be totaled from the crash or totaled from being chopped, and simultaneity isn't a problem anymore. If the train is shorter than the tunnel, it crashes into the guillotine and if it is longer it gets chopped.
if you consider that in the reference frame of the person that the train is traveling relative to, the train gets smaller and from that of the person on the train the tunnel gets smaller so from the reference frame of someone analysing the experiment, both the tunnel and the train gets smaller but the rapport between their lengths stays the same. That to say if the guillotine was set to come down after the train went through the tunnel it would neither chop the tail nor the front of the train, since from the point of view of the guillotine's blades, the train gets smaller because it was moving relative to the blades.
well the guillotine on the right would come down in front of the train and the train would crash into it, but the shockwave from that collision can only travel as fast as the speed of light so by the time the crash effected the back end, it has already made it to the second guillotine, so that in turn comes down after the train has passed it. so pretty much the same as both events, but involving a crashed train. hope this helped
This thought experiment is an excellent example that illustrates the need to be careful when doing special relativity. The analysis from the point of view of the hill is easy, and it gives the correct result, but the issue of relativity of simultaneity makes the analysis from the train's point of view a bit more complicated.
One can use the minkowski diagram to solve this problem.
Just a thought here: It's just like sound, that's due to the finite speed. If you change the guilliotines with sound systems, the guy watching will hear the sound of both at the same time, but the guy on the train will hear one and then the other.
I think once the train collides with the first guillotine the train is no longer moving and so the tunnel and the train are then in the same inertial frame. This means that in any frame the lengths of the train and the tunnel are the same and so when the second guillotine strikes nothing happens. So whichever reference frame you're in, you see the same thing.
i don't quite understand what you are implying. i would think matter affects time because time is based on matter and its movements/changes. matter seems to have a pull on space-time and we see evidence of those distortions everyday
The distortion of size occurs in the direction of movement, so it will change over time. Each cart will see itself approaching a tunnel too narrow for it, but then changing shape to fit around them. I think.
Try thinking about this if you were to put in a small neutron star or BH along with its time dilation effects, then note if its extreme enough you could actually walk to the other side to let a longer object out.Works into a really good theory to explain how the universe started but its too much for here.Its postulate is that time dilated contraction of matter is indistinguishable from space expansion and shows a testable way of showing that space expands around any gravitational object.
In the concept of relativity of simultaneity, why must the gillotine in the front of the tunnel is dropped and raised before the gillotine in the rear of the tunnel is dropped and raised? Also doesn't this mean that length contraction is only an apparent effect since the train comes out of the tunnel unharmed?
Another question, relating Lorentz contraction: If you see distances squashed in a certain direction when travelling at relativistic speeds, then aren't you able to figure out your absolute movement (as if the universe had an actual absolute axis of reference) by noticing that the atoms are much closer together in a certain direction than in others?
How long do objects appear in the opposite direction of the motion? Do they get longer? If the contraction occurs only in the direction of movement, then the Trainspotter had to be standing by the rightmost exit of the tunnel, as the train was rushing towards him, not away from him. Then when he pushed a button to activate the guillotines, the further one on the left did in fact come down later because of the delay on the cable.
Objects travelling near or at the speed of light warp local space. So yes, what you're saying really does happen. Why do you have a problem with this? Warping space =/= warping the material the train is made out of.
The tunnel and the train are the same size no matter the speed of the train. The train may grow slightly from friction and the heat causing the metal to expand. The shock wave created in front of the train may decimate the tunnel at high enough speeds, but nothing changes the size of either object. The guillotines are the key to making this work. If the train were moving 1 cm per year along the track, it would be easy to get to a point where the guillotines could close, enclosing the train and open in time to let the train out. However, the faster the train goes, the more difficult it becomes to close and reopen the guillotine in time due to the mass of the guillotines. The energy required to move the guillotines down and up in a fraction of a second is enormous, plus, the materials that make up the guillotine might not be strong enough to withstand the forces needed to move them that quickly.
If you move at constant velocity = v, then it would shrink ,x=x'√(1-v^2/c^2 )
x is the distance when moving, and x' is the distance when the object is not moving.
It would matter where the person on the train was sitting. If he was in the middle, perhaps the tunnel in front would appear compressed, but then the rear of the tunnel would have to be stretched. So when he is half way through (or less) he pulls the blades down becausu there is more room to the back of the tunnel
A lot of people here are asking what if blades never go up. And they get "train crashes int second blade" as an answer.
While the real question is "Suppose train is actually longer that tunnel, and get shrinked, fits into tunnel and crashes into second blade, what happens next, assuming the blades are infinitely more sturdy than the train?"
From outside point of view, the whole train went inside tunnel, then crashed. How come it's still inside the tunnel, between closed blades, distance shorter than length of the train?
From train's point of view, moving tunnel gets even shorter. The head of the train reaches exit and suddenly crashes into second blade while the tail is still outside of tunnel. Shouldn't then the tail stop and be cut off by the first blade?
The answer is, signals propagate with finite speed of light, thus by the time signal about crash (either warning message or wave of structural damage) reaches the end of the train, it will already be inside the tunnel.
The back gets chopped off in neither. From the perspective of the person on the train, the train will smash into the first guillotine that comes down; the one at the end of the tunnel. Now that it has crashed into the guillotine it is no longer moving, meaning the tunnel is no longer compressed. As the tunnel is no longer compressed, due it being stationary fro the train's frame of reference, the second guillotine will fall harmlessly.
No one said time is a measure. "Time" is part of space-time, and has nothing to do with assigning values to intervals between events. That might be how we perceive time, but time is itself a dimension of space-time that has to do with causality; it determines that the "past" is the set of events that can send information elsewhere, while the "future" is the set of events to which information can be sent.
An inadequate explanation, tbh, but hopefully sufficient.
In fact, the main lesson of relativity is that all reference frames are equally valid. There is no "correct" reference frame. The equations of Einstein's relativity allow one observer to determine what another observer will observe. Like the professor said, there is no "fact of the matter." One person sees this, another sees that, and they are both right as long as their observations are related by relativity.
This is not about having imprecise measurements. Even with perfect measurements the disagreement about what happens still exists. It´s not just like a lens distorting our view of the world. In relativity, the world actually does get distorted.
i just love the fact that he is so voluble, he goes on and on about it without taking a breath!
In order for the left cleaver to "trigger" the right cleaver, it would have to send a signal that could travel no faster than the speed of light. But the front of the train would reach the right end of the tunnel before any lightspeed signal could travel from the left end to the right end triggered by the back end of the train entering the tunnel, so the front would get chopped from both points of view.
I may be wrong, but I believe that the train observer will see the signals moving from each guillotine at different speeds, such that they will arrive at chip at the same time. The important thing here is not the timing of the switches, but the timing of the signal arriving at the chip. However, both will agree that there was a light.
This guy is the first person I've seen who's managed to answer my questions about relativity to my satisfaction.
My guess is that the train collides with the front guillotine and stops. No more contraction of the tunnel because it's not moving, so it's the same length as the tunnel and can fit inside. So when the back guillotine comes down it misses the back end of the train.
just a minor correction: the wave produced by the impact would not travel at the speed of light it would travel at the speed of sound. The train would be long gone by the time the back end felt the crash.
The way I see it: If the train is moving near light speed, then to an observer on the train after the observer passes through the tunnel entrance the portion of the tunnel between the observer and the entrance would stretch. So at the moment the front of the train is near the tunnel exit the tunnel has elongated to encompass the whole train.
Follow up question for the Professor: What if one of the guillotines is the cause for the other to fall ? Shouldn't they then fall in the same order for all observers independently of the frame of reference?
Great lecture in special relativity. This is the first fast speaking guy I ever undserstood.
It's the same problem, when the guillotines come down simultaneously in one reference frame, the other frame will have the from one come down, and the back one will come down when the train crashes into the front one, slightly later