The Real Twin Paradox | Doc Physics

This emphasizes just how funky time dilation can be. It's also a cool example of real time travel. Unfortunately, I believe the paradox here is not often understood. The fact that they experience time differently is NOT the paradox. The paradox is that (on first glance) each twin witnessed his twin doing the exact same thing. So the concern is: HOW DID THE UNIVERSE CHOOSE WHOSE TIME TO MAKE SLOWER WHEN THEY FINALLY GOT BACK TOGETHER. The answer is hidden - try to find it. Don't put it in the comments, though. Explanations are easy to find elsewhere if you need them.

[@DocSchuster]

I am often playing a joke, but not now. I suggest thinking about this problem while watching my video that introduces Einstein's thought process when developing special relativity. I also left a verbal clue in this video, but it's easy to miss if you're not REALLY careful. It's a SPECIAL clue.

[@DocSchuster]

Thank you! I'll pay more attention to that in future videos. If I get the closed-captions corrected, would that help, too?

[@iwilldi]

Let there be an equilateral isoceles triangle A B C, where BC is 1 lightyear and AB = AC = 1 million lightyears Let A be a pulsar which can be allways detected und the pulses counted. Let the earthling stay at B and let the traveller make his way from B to C und back to B as fast as he wants. When both meet again, they will agree on the pulsar-signals they counted during the voyage of the traveller. Almost perfect objective clocks do exist. SRT is broken.

[@DocSchuster]

B Sto Do you know what equilateral means?

[@iwilldi]

sorry, i meant an isosceles triangle, you are right.

[@DocSchuster]

B Sto This is a clever problem. I do not immediately see the solution. I wonder what someone smarter than me will say!

[@WarmWeatherGuy]

I was confused about that until I found out that the whole thing can be explained with only special relativity. Of course the acceleration is a factor but presumably not significant. In the class I took we just ignored the acceleration and pretended the twin could turn around in an instant. Also, to calculate the age difference we only use speed and distance, not acceleration.

[@DocSchuster]

This video IS A MESS! I was trying to decide how long to let Cody travel, but I changed my mind in the middle. This is an excellent candidate for a remake. Thanks for the tip.

[@DocSchuster]

Good. You are at the point of seeing why this is a paradox. Upon first glance, it appears as if both perspectives are equally valid, and each twin should see the other as much younger than himself. Obviously, this cannot be the case if they are both together again...

[@Plowned]

ARE YOU READY FOR THE PARADOX??! .....ok

[@sc-ek6qz]

Haha...

[@sc-ek6qz]

At 5:42 mark...

[@PLazzar]

The formula is wrong. It should be Zack's time divided by gamma not multiplied by gamma to arrive at Cody's time. Also your answer to Grizzly Fuzz is wrong too. The light frame would not experience distance either.

[@DanielFelsen]

Doc Shuster, thank you for these great videos, making physics accessible to us nonscientists. At 3:18, you say that Cody’s time interval (as seen by Zach) is Zach’s time interval times 2, but I think you meant to say that, as viewed by Zach, with Cody’s traveling at 0.87C, Cody’s time interval is one-half of Zach’s time interval. In other words, from Zach’s reference frame, if Zach experiences 20 years then Cody experiences half of Zach’s time interval, or 10 years.

[@DocSchuster]

It sounds like you're exactly correct. Thank you! I need to remake this video for sure. I confused myself in the middle.

[@dumitrufrunza8136]

Daniel Felsen Doc Schuster seems to be correct when he says "Cody’s time interval (as seen by Zach) is Zach’s time interval times 2", or in equation form _delta_t_ = _delta_t_naught_ * 2. The confusion arises, I think, from the temptation to substitute 20 yrs for _delta_t_naught_, get the result _delta_t_ = 40 yrs, and then conclude that Cody spent 40 yrs in space. _delta_t_ is and _delta_t_naught_ are defined as ticks on Cody's clock and Zach's clock respectively. What the equation says is that "1 tick on Cody's clock equals 2 ticks Zach's clock". In other words, it takes 2 ticks of Zach's clock to make 1 tick of Cody's. Another way of putting this is that Cody's time runs slower than Zach's - twice as slower. To illustrate this, take 1 tick = 1 second, and suppose that right before Cody's departure, their clocks where synchronized to 12 o'clock. Zach looks at his watch - 1 second passed; on Cody's watch, only 1/2 second passed. Zach - 2 seconds; Cody - 1 second; Zach - 3 secs; Cody - 1 1/2 secs; Zach - 4 secs; Cody - 2 secs, etc, etc. If you do this exercise with 1 tick = 1 year, then when Zach counts 20 yrs, Cody will count 10 yrs : all good.

[@mgominasian9206]

Daniel Felsen yeah but who is actually the the proper time T0,and the dialted one T

[@DanielFelsen]

Dear Mgo: I provide a long explanation below in order to give as much detail as possible. First, Doc Schuster has confused Zach and Cody when applying their time measurements to the time-dilation equation. [See the exchange between Doc Schuster and me in a post below. In that exchange he confirms that my equation is correct and that I have correctly applied it to Zach and Cody.] Second, you can write the time-dilation equation several different ways, all of which are equivalent. Because people often get confused over who T is and who T naught is (or who T1 is and who T2 is), I like to use descriptive words. One way to write the equation is T for proper-time person = T for other person TIMES the SQUARE ROOT of (1 MINUS [v squared / c squared] ). An equivalent way to write it is T for other person = T for proper-time person TIMES (1 DIVIDED BY the SQUARE ROOT of (1 MINUS [v squared / c squared] ) ). It’s much easier to express this in math symbols than words, but I can’t do it in these comments. Let’s use the first equation: T for proper-time person = T for other person TIMES the SQUARE ROOT of (1 MINUS [v squared / c squared] ). Third, you are correct that one must correctly identify who is the “proper-time person” and who is the “other person.” Proper time is the time duration (interval) between events in the reference frame where the events happen at the same place. The two events are the start of the time interval (Event 1), and the second event is the end of the time interval (Event 2). The person who measures proper time measures the two events at the same place, using a watch on his or her wrist. That’s why many people call proper time “wristwatch” time. Fourth, in Doc Schuster’s example, Zach stays on Earth and Cody goes in the rocket. There are two legs to Cody’s trip. The first leg is while Cody travels away from Earth for 10 years, as Zach measures time. The second leg is when Cody travels back to Earth for 10 years, as measured by Zach. The question is how much time has Cody experienced, as measured by Cody? Let’s just look at the first leg of the trip, and then we’ll double the results to account for both legs of the trip. Fifth, as measured by Zach, Cody is measuring proper time because Cody measures the time duration (interval) between events in the reference frame where the events happen at the same place: the start of the time interval (Event 1) and the end of the time interval (Event 2). Cody uses the same clock (the watch on his wrist) to measure Events 1 and 2, and therefore Cody measures proper time. For Cody, both events happen at the same place; Cody measures both events by looking at the watch on his wrist. Note that, in this scenario-where we’re looking at things from Zach’s perspective-Zach does not measure proper time. For Zach to measure the start of the time interval for Cody and the end of the time interval for Cody, Zach would have to use two different clocks because for Zach, Event 1 and Event 2 happen at different places. For Zach, Event 1 happens right near Earth (when Cody starts the first leg of his trip) and Event 2 is the end of the first leg of Cody’s trip, which is very far away from Earth. Zach would have to use two different clocks to measure both events. Again, Cody is using only one clock-the one on his wrist-to measure both events, and that’s why Cody is measuring proper time. Sixth, now let’s plug in the information to solve the time-dilation equation, knowing that Cody is measuring proper time. In the example, the relative speed between Zach and Cody is 87% of the speed of light, or 0.87c. T for proper-time person = T for other person TIMES the SQUARE ROOT of (1 MINUS [v squared / c squared] ). T for Cody = T for Zach TIMES the SQUARE ROOT of (1 MINUS [(0.87c) squared / c squared] ) T for Cody = T for Zach TIMES the SQUARE ROOT of (1 MINUS [0.7569c squared / c squared] ) T for Cody = T for Zach TIMES the SQUARE ROOT of (1 MINUS 0.7569) T for Cody = T for Zach TIMES the SQUARE ROOT of (.2431) T for Cody = T for Zach TIMES 0.49 Rounding 0.49 to 0.5, we get: T for Cody = T for Zach TIMES 0.5 This means that Cody measures time progressing half as fast as Zach measures time progressing. [Note that this is what Doc Schuster said in his video, though his written equation was wrong.] For the first leg of the trip, Zach measures 10 years. Let’s plug this into the equation to determine how much Cody measures for the first leg of the trip. T for Cody = T for Zach TIMES 0.5 Substitute T for Zach = 10 years T for Cody = 10 years TIMES 0.5 T for Cody = 5 years So, from Zach’s reference frame, Zach measures that the first leg of the trip takes 10 years and Cody measures 5 years. We can double these results to account for both legs of the trip, and in that case Zach measures that the total time for both legs of the trip takes 20 years and Cody measures 10 years. Now, here’s the really interesting twist. In the scenario discussed above, Zach (who remained on Earth) considered himself as staying “still” (meaning Zach’s velocity = 0 mph) and Cody as moving (meaning Cody’s velocity = 0.87c). But because there are no privileged reference frames in special relativity-where the reference frames are moving at constant velocity (meaning no changes in speed or direction)-Cody can consider himself as staying “still” (meaning Cody’s velocity = 0 mph) and Zach as moving (meaning Zach’s velocity = 0.87c). In this second scenario, Zach would be measuring proper time because Zach measures the time duration (interval) between events in the reference frame where the events happen at the same place: the start of the time interval (Event 1) and the end of the time interval (Event 2). Zach uses the same clock (using the watch on his wrist) to measure Events 1 and 2, and therefore Zach measures proper time. For Zach, both events happen at the same place; Zach measures both events by looking at the watch on his wrist. So, in this new scenario, we can plug in the information to solve the time-dilation equation, knowing that Zach is now measuring proper time. In the example, the relative speed between Zach and Cody is 87% of the speed of light, or 0.87c. T for proper-time person = T for other person TIMES the SQUARE ROOT of (1 MINUS [v squared / c squared] ). T for Zach = T for Cody TIMES the SQUARE ROOT of (1 MINUS [(0.87c) squared / c squared] ) T for Zach = T for Cody TIMES the SQUARE ROOT of (1 MINUS [0.7569c squared / c squared] ) T for Zach = T for Cody TIMES the SQUARE ROOT of (1 MINUS 0.7569) T for Zach = T for Cody TIMES the SQUARE ROOT of (.2431) T for Zach = T for Cody TIMES 0.49 Rounding 0.49 to 0.5, we get: T for Zach = T for Cody TIMES 0.5 This means that Zach measures time progressing half as fast as Cody measures time progressing. For the first leg of the trip, if Cody measures 5 years, Zach measures only 2.5 years. Here’s the calculation. T for Zach = T for Cody TIMES 0.5 Substitute T for Cody = 5 years T for Zach = 5 years TIMES 0.5 T for Zach = 2.5 years So, under this second scenario as measured from Cody’s reference frame, Cody measures that the first leg of the trip takes 5 years and Zach measures 2.5 years. We can double these results to account for both legs of the trip, and in that case Cody measures that the total time for both legs of the trip takes 10 years and Zach measures 5 years. Finally, you might want to say that, since there are no privileged reference frames in special relativity, the twins should be the same age when they get back together on Earth. But the scenario that Doc Schuster presented (the Twin Paradox) is not really a paradox at all. Zach’s reference frame remained at a constant velocity, meaning no changes in speed or direction. (Of course, the Earth does change direction, but it is relatively minor for purposes of special relativity.) Cody, however, was not in a constant-velocity reference frame. When he started his trip he accelerated his rocket (a change in speed) to get to speed 0.87c. Then, before he got to the end of the first leg of his trip, he decelerated (a change in speed) so he could turn around (a change in direction) and then accelerated again (a change in speed) to 0.87c for the return trip. And Cody had to decelerate (a change in speed) to 0 mph in order to stand next to Zach on Earth. So, one must use general relativity to account for the changes in speed and direction. I hope this explanation helps.

[@mgominasian9206]

Yeeah man it did thanks a lotttttt

[@david_porthouse]

The worldline with the kink in it is the one whose clock runs slower in aggregate. This is just the hyperbolic triangle inequality. The kink cannot be eliminated by a Lorentz transformation. Compare to the elliptical triangle inequality, which is unaffected by a rotation. This isn’t a difficult subject.

[@josephcraker8539]

6 people are slackers, leaning back and folding their arms

[@ManiekGra]

Although what I will say now will sound as a complete nonsense and it probably is, I want to share this with the Internet here. The alternative explanation (although unlikely and crazy) is this: Everyone of us lives in a separate copy of a universe, where you are always at rest. There is an easy way to prove or disprove this theory, but to do this you would have to be on that SR-71 airplane mentioned in the video with the atomic clock. There is a chance, that after landing back you would be shocked to find that the clock on the Earth behaved like it would actually slowed down (because it has been moving relatively to YOU, the center of YOUR universe). And everyone else in that YOUR universe would see the same thing (so they would not tell you that you are nuts). On the other hand, if YOU will stay on the earth during this experiment, the clock on the plane will be moving relatively to YOU so the clock on the plane will slow down. The pilot of that airplane will see the slowdown too, because this is your universe, not him and every single thing in this universe moves relatively to YOU, so the result of the experiment depends on: where you were during it. In his (the pilot) own universe things will go the other way. So the only way to check this is to do the experiment by yourself and somehow move with the clock (you don't need to pilot the plane, just move with the lock). Put one clock on earth, get another one to a plane, after landing back, compare the clocks. Unfortunately if what I am saying is the truth (I am aware it sounds completely crazy), everyone else who will perform this experiment in YOUR universe and write about it, will report the normal slowdown of the clock on the plane (because the clock moved relative to YOU so the dilation occured). The only way to get a different result is to do the experiment by yourself. If you even understand what I have been trying to say here, I am impressed, because it's completely crazy, although it may be possible. But what if the experiment was performed before you were born? :X

[@jimdogma1537]

Thought experiment question: Say you have two travelers starting from the same point, each of which moves away from the other at .4c, so their relative velocities differ by .8c. Say they are both 20 years old. At the end of 10 years how old will each be relative to the other? Question 2. Now say that these same brothers, after their 10 year journey, turn around and start heading back toward each other at the same rate? 10 years later they pass each other at the same point they began their journey at and hold up their clocks to each other. What time does each read? The null hypothesis would seem to be that they'd read the same time, but each brother has been traveling relative to the other at close to the speed of light for 20 years, so from the perspective of SR you'd think there'd be a large difference on their clocks.

[@DocSchuster]

Symmetry answers the second question for us, but I think the first one is ill-posed, since their age depends on measurement by the observer, which takes time. That's what makes this an interesting subject!

[@massimilianodellaguzzo8571]

Hi Doc Schuster, in my opinion there is no symmetry between the twin astronaut and the twin left on Earth. (astronaut twin is younger if he moves at a speed v with respect to the Earth ) On the other hand if the astronaut twin launches a rocket (at speed v with respect to the spaceship and towards the direction in which he sees the Earth moving away), then the rocket is younger than the astronaut twin.

[@kitchan3166]

Hi Doc hv a stupid question at 0.87 c time c = time z * 2 therefore every 1 unit of time passed for Colby can written as 1/2 = time z hence colby clock is ticking quicker than zack, I found this so confusing

[@brochachoiii6657]

Zach is actually 10 years older, because the years were being based off time relative to Zach. So Zach would be 10 years older, and Cody would only be 5 years older.

[@LifeByChocolates]

There is no paradox. You just have to remember that it isn't space that the twins are traveling through but space-time. The earth bound twin remains in a constant velocity frame while the the one in the rocket is accelerating. Here are two very clear explanations. www.cpp.edu/~ajm/materials/twinparadox.html And this one which has more math but the diagrams aren't as cool: math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_spacetime.html (I hope I didn't give anything away.)

[@Jaidip76]

What happens if we take the case of one twin only moving towards you without any acceleration?how will he perceive your time and you his? Or take the case of both travelling to distant planet at different speed.

[@leonard1871]

The problem here is the changing reference systems , the twin on earth assumes the one in the spacecraft maintains a linear route to his destination , while the twin in the rocket doesn't ( he turns around and acquires if you will a different reference frame from the one he had before ) hence the paradox

[@PaulMarostica]

To Doc Schuster: In the typed introduction to this video, I didn’t like that you weren’t going to explain the answer to the paradox. It seemed lazy. But when the video ended, and you challenged your viewers to determine the answer themselves, I very much liked it. Why? Because most often in learning theory, a teacher tells students a theory’s assumptions, then tests the students on the theory’s implications. Instead, here, each viewer is challenged to determine their own assumptions. This gives each viewer an opportunity to be a real science theorist. Trying to invent a theory is a very different experience from trying to use a theory. I think all science students need much more practice in trying to invent theories. Why? Because it is technologists who use theories. It is scientists who invent them. I have been independently solving fundamental physics theory problems for over 30 years. I think relativity theory, and its attempted solutions to its own twin paradox, are physically illogical. I think I have invented a better, physically logical theory. Doc Schuster, I offer you, along with anyone else who might be interested, an opportunity to test the limits of your understanding of relativity theory with the help of my KZbin video, "You’ve Learned Relativity Theory". I’m very curious to learn what you think. You can find my videos using the 3 search keywords: matter theory marostica.

[@briz1965]

you didn't tell the plebs the answer

[@wenniezhao9835]

By using the time dilation formula, u have to choose a space-time coordinate system, in which one is stationary and one is moving. This coordinate system here is the earth space-time. In our real life, GPS has already told us the paradox as the video claimed didn't happen. The atomic clock carried by Satellites always moves slower than the atomic clock on earth. That's why we have to synchronize them constantly to make GPS work functionally, or it will drift miles a day and will be totally useless.

[@joses1881]

We can do away with the acceleration asymmetry pretty easily. Both twins take off in rockets in opposite directions, and come back after N years. Note that N can be as big as we want. Now you have an interesting paradox, and I haven't seen a simple intuitive explanation of how it would work. Presumably the acceleration phase is when the twins catch up. But how would the effect of the acceleration cancel out N years of travel, where again, N can be anything?

[@allorgansnobody]

+Jose S I drew up a space-time diagram for this (something you ought to google, very useful for answering all questions such as these) and I believe that if both accelerate away and return in opposite directions with perfect symmetry then both of their times will be dilated equally relative to some who say, stayed in a stationary rocket at the starting point. tl;dr they don't dilate relative to eachother

[@hdthor]

There’s no paradox, they would be the same age.

[@DanielFelsen]

Doc Schuster, I’m having trouble understanding your time-dilation equation. (I wasn’t sure whether to post this on the previous video or this one.) When I do the derivation myself (and as I believe my text confirms, assuming I’m understanding it correctly), I determine that the “stationary” observer (the person on the Earth) finds that a time interval for the “moving” person (the rocketeer) equals the “stationary” person’s time interval TIMES the square root of (1 - (v squared / c squared) ), but your calculation is different. You calculate that the time interval for the “moving” person (the rocketeer) equals the “stationary” person’s time interval DIVIDED BY the square root of (1 - (v squared / c squared) ). For example, assuming the rocketeer is moving at .87C (as measured by the Earth-bound observer), then, if the Earth-bound observer experienced a 20-year time interval (from his or her perspective), then, using my version of the equation, the rocketeer’s time interval would be equal to the Earth-bound observer’s interval (which is 20 years) TIMES the square root of (1 - (.87c squared / c squared) ), which is 20 years TIMES (approximately) 0.5, which is 10 years. My result agrees with yours, but our equations seem to be different. (If I’m calculating properly, your equation - 20 years DIVIDED BY the square root of (1 - (.87c squared / c squared) ) - would yield a time interval of 40 years for the rocketeer, as measured by the Earth-bound observer.) Sorry this is so verbose.

[@DocSchuster]

I appreciate your question. Time dilation must be done carefully. It means that the observer sees the clock that is zooming by have longer time intervals, which means that the same observer will see that the zooming clock has recorded fewer of those longer time intervals. It's in that sense that time is dilated - it's stretched. If you also consider carefully who has the proper time (the longest time between two events), you can't go wrong. That punk kid gets the t_naught.I agree with your calculation of time dilation. The observer will always perceive more time to have passed than the observed if they have a relative velocity.

[@maljamin]

Aw man, it wasn't supposed to be 10 years experienced by Cody, it was supposed to be 10 years as literally measured by Zach. So that's just 10 years for Zach and 5 for Cody. Things are jumping around as far as time elapsing relative to whom. Because we're jumping between the happening-as-observed and the "for-cody-as-observer". One is measuring for ourselves one is modeling for another. So this gets out of hand but at LEAST you hit the actual paradox. There's even a Neil DeGrasse-Tyson video out there where he totally skips the actual paradox.

[@noilet]

Thank you for this video. Alot of other youtube videos doesn't explain the paradox itself, they just explain how the twin who travels will be younger than then other when he gets back, and they call THAT a paradox. Pretty rediculous.

[@WideCuriosity]

They call that solving the obvious paradox. The issue is though, that not all explanations agree. For ages I though acceleration was the crux of the solution. I'm now thinking that only plays a part in bringing a second meeting where the effect from other causes, and the misunderstanding of what is happening in each time frame, can be confirmed. But I'm still far from being clear about it.

[@wenniezhao9835]

Like us on earth, I'm standing there and a car is moving away from me. If I only compare the car and myself, I can't tell which is moving. But if we look at a tree, a building or the ground, introducing in the third common reference (earth space coordinate system), then we know it's car moving. For time dilation matter, time is another variable dimension, so we introduce in earth space-time coordinate system

[@kanepovey2781]

Special relativity does not apply because when Cody turns around he changes direction therefore accelerating and special relativity does not apply in acceleration which proves that Cody is in fact the one who is moving and younger

[@mikegale9757]

The doc asks us (in the video description) to refrain from posting answers to his question, but riddle me this. Who's younger at the reunion if both twins go walkabout with equal and opposite velocities? Bonus points if you can calculate the age discrepancy for arbitrary velocities.

[@stewiesaidthat]

@silverrahul do it with two plants. Which one is younger? The one in motion following the sun so that it is always 12 noon or the one that experiences a 24 hour day/night cycle.

[@-Pentcho-Valev]

" The paradox is that (on first glance) each twin witnessed his twin doing the exact same thing. So the concern is: HOW DID THE UNIVERSE CHOOSE WHOSE TIME TO MAKE SLOWER WHEN THEY FINALLY GOT BACK TOGETHER." On second (and final) glance, the paradox is an absurdity: Einstein's relativity predicts that the travelling twin returns both younger and older than his sedentary brother. In order to confuse the critics, Einsteinians teach two things: 1. The youthfulness of the travelling twin has nothing to do with the turn-around acceleration suffered by him/her: www.symmetrymagazine.org/article/may-2014/the-twin-paradox Fermilab physicist Don Lincoln: "Some readers, probably including some readers who hold doctorates in physics, will claim that the difference between the two twins is that one of the two has experienced an acceleration. (After all, that's how he slowed down and reversed direction.) However, the relativistic equations don't include that acceleration phase..." sciencechatforum.com/viewtopic.php?f=84&t=26847 Fermilab physicist Don Lincoln: "A common explanation of this paradox is that the travelling twin experienced acceleration to slow down and reverse velocity. While it is clearly true that a single person must experience this acceleration, you can show that the acceleration is not crucial. What is crucial is that the travelling twin experienced time in two reference frames, while the homebody experienced time in one. We can demonstrate this by a modification of the problem. In the modification, there is still a homebody and a person travelling to a distant star. The modification is that there is a third person even farther away than the distant star. This person travels at the same speed as the original traveler, but in the opposite direction. The third person's trajectory is timed so that both of them pass the distant star at the same time. As the two travelers pass, the Earthbound person reads the clock of the outbound traveler. He then adds the time he experiences travelling from the distant star to Earth to the duration experienced by the outbound person. The sum of these times is the transit time. Note that no acceleration occurs in this problem...just three people experiencing relative inertial motion." www.damtp.cam.ac.uk/research/gr/members/gibbons/gwgPartI_SpecialRelativity2010.pdf Gary W. Gibbons FRS: "In other words, by simply staying at home Jack has aged relative to Jill. There is no paradox because the lives of the twins are not strictly symmetrical. This might lead one to suspect that the accelerations suffered by Jill might be responsible for the effect. However this is simply not plausible because using identical accelerating phases of her trip, she could have travelled twice as far. This would give twice the amount of time gained." 2. The youthfulness of the travelling twin is entirely due to the turn-around acceleration suffered by him/her: en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity Dialog about Objections against the Theory of Relativity, 1918, Albert Einstein: "During the partial processes 2 and 4 the clock U1, going at a velocity v, runs indeed at a slower pace than the resting clock U2. However, this is more than compensated by a faster pace of U1 during partial process 3. According to the general theory of relativity, a clock will go faster the higher the gravitational potential of the location where it is located, and during partial process 3 U2 happens to be located at a higher gravitational potential than U1. The calculation shows that this speeding ahead constitutes exactly twice as much as the lagging behind during the partial processes 2 and 4." www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spacetime_tachyon/index.html John Norton: "Then, at the end of the outward leg, the traveler abruptly changes motion, accelerating sharply to adopt a new inertial motion directed back to earth. What comes now is the key part of the analysis. The effect of the change of motion is to alter completely the traveler's judgment of simultaneity. The traveler's hypersurfaces of simultaneity now flip up dramatically. Moments after the turn-around, when the travelers clock reads just after 2 days, the traveler will judge the stay-at-home twin's clock to read just after 7 days. That is, the traveler will judge the stay-at-home twin's clock to have jumped suddenly from reading 1 day to reading 7 days. This huge jump puts the stay-at-home twin's clock so far ahead of the traveler's that it is now possible for the stay-at-home twin's clock to be ahead of the travelers when they reunite." gjl038.g.j.pic.centerblog.net/3fea2faf.jpg

[@DocSchuster]

Pentcho Valev Please accept my apology for not analyzing your arguments. I have a busy week and weekend coming up! Keep 'em coming.

[@HarshColby]

Einsteinians? According to Special Relativity, the first point is correct and the second is wrong. "Einsteinians" wouldn't make point two. The first of your two "supporting" references doesn't support statement 2. "Dialog about objections..." talks about General Relativity, not Special Relativistic time dilation. The John Norton quote is just plain wrong.

[@IllAdvisedHooligan]

Correct me if I'm wrong, but the rocket encounters a non-inertial frame of reference three times.. Not twice. Take off, change of direction, but if r are counting take off as non-inertial wouldn't the landing also? Anyways the non-inertial moves the rocket twin away from special relativity back to general relativity, therefore when he returns he will appear younger to the earth twin, and view the earth twin as older. Please correct any misconceptions that I have.

[@philochristos]

I've watched a few videos on the solution to the twin paradox, and it seems like even the physicists themselves disagree on what the solution is. One physicist said the solution lies in the fact that when Cody turns around, he has to slow down and accelerated in the process, changing the apparent field of gravity in his frame of reference, which causes the difference. Another physicist argued that Cody's acceleration is irrelevant to the problem, and he came up with a thought experiment to prove it. He said the solution lies merely in the fact that Cody's frame of reference is different in the outgoing trip than it is in the incoming trip.

[@vipinchandra7785]

Cody changes frame of references...but Zack remains in his frame...here is the mistake done by Cody...the two frames are moving in different directions and thus they say different time appear on the earth

[@philochristos]

@@vipinchandra7785 But if motion is relative, then I don't see the difference between saying Zach stayed put while Cody went out and back again and Cody staying put while Zach went out and back again. From Zach's point of view, Cody was in two frames of reference, but from Cody's point of view, Zach was in two frames of reference. To say that one changed frames of reference is to assume some objective frame of reference, but I was under the impression that special relativity denied there were any objective frames of reference.

[@Guarrdian1984]

@@philochristos Exactly! Cody can say Zach's frame of reference also changed from one direction to the opposite so that's not the solution!! I don't understand why famous physicists cannot easily solve the paradox and they still struggle...

[@haiderrehmanbutt720]

What I can see is that when the rocket takes off to approach 0.87c, it is a non inertial fram of reference, so is the case when it turns around and when it finally stops back a t Earth. We are kinda jumping into General relativity (which I know nothing about). W just violated the first of Einstein principle.

[@DocSchuster]

Haider Rehman Butt YES! You've found the error!

[@NihongoWakannai]

+Doc Schuster but what if the rocket never turns around? what if it keeps moving in the same direction, but they argue about who is older by sending messages to eachother

[@vaishnavkumars9261]

+Haider Rehman Butt i cant get you pls explain me

[@sunjen11]

Check out the Twin paradox video from Fermilab. It states that accelleration is not the underlying reason of time dilation. If the ship always goes 0.87c and takes a big long arc to come back, it changes reference frames when it comes back so upon arriving and comparing ages they agree the rocket twin is younger. Take note that while on travel they don't agree on their ages.

[@maersklandro]

Just because clocks appear to run slower doesn't mean time actually is. If time really did run slower the closer to the speed of light you are traveling then you would be effectively going back in time as you travel. Then, when you return to earth or arrive to your destination you would then be in the past of people who never left or traveled. So people back home would not be 20 years older but just 10. Just like you. Or else you'd have somehow skipped ahead 10 years in an instant upon your ceasing to travel. But if you did not skip ahead 10 years of Earth time upon your return then you would be interacting and interfering with the past of present people on Earth. So either time travel into the past is possible by simply accelerating and decelerating or you skip ahead 10 years but then people on Earth are actually interacting with your past and interfering with it. Either way it implies that objects in the present can interact with objects in the past and so interfere with the past of present objects and possibly alter the present or create parallel universes wherein the past and present are different. Of course, this effect would not be contained and only apply to travelers travelling at relativistic velocities but would affect everything which accelerates and decelerates at all. Furthermore, the exact same problem affects the Alcubierre drive. How do you get out of the space bubble to actually arrive at your destination without collapsing the bubble and being taken right back to where you left from or having to travel through the compressed space ahead of you as if it were normal space for you. Relativity is either broken or requires an absolute space and time frame.

[@DocSchuster]

***** " time travel into the past is possible" Yes! But you'll have to leave notions of absolute time behind. Thankfully, though, causality is still preserved. In fact, relativity is needed in order to preserve causality. Keep thinking about it - it's worth quite a bit of your attention.

[@39knights]

I posted a video where I assume the rocket with the twin is in an asynchonous orbit with the equator of the Earth, second twin standing at the equator watching his twin in space. If we use 0.87c for ease of calculation then the orbit needs only be about 1/3 of a light year out. All frames of reference being equal, the twins would have to think they are stationary to each other though one is traveling at 0.87c. How would this theory play out then? Even their light clocks would appear the same. Now place another non-rotating observer at the North Pole observing the twins and a real paradox develops. Since the twins experience the same referential frame they would see each other age the same. The North Pole observer should witness a 2:1 ratio between them. Run it for ten years and then have all three stand together and argue over it.

[@DocSchuster]

39knights I think you mean that the rocket is in a synchronous orbit. If that is the case, the rocket will be accelerating at v*v/r, which is 21 m/s/s if we use your 1/3 ly approximation for radius. These frames are most definitely not equivalent, because one guy is accelerating while the other is not (much).

[@39knights]

You can only say that they are not equivelant because you are able to take the 'absolute' viewpoint. From within the thought experiment the frames of reference are as I stated. In the 'real' Universe the Earth revolves around the Sun, which revolves around the MilkyWay, which possibly revolves around some much larger system. Without falling totally into absolute relativism, who can say that any of our straight-line experiments or experiences are actuallly straight. It seems our whole Universe revolves rather than participates in straightline motion. Whether it is straight or curved, from within the experiment itself, it is possible to create a situation where 2/3 of the observers 'appear' to be in the same reference and 1/3 of the observers can take a virtual 'absolute' position which totally contradicts the others. It would also be possible to do this experiment (assuming we can eventually reach the space travel speeds being proposed) within a lifetime and within an observable distance.

[@39knights]

39knights Perform the experiment for 5 years on 5 year old twins. Assuming 0.87c and a 2:1 ratio of time dilation I am wondering if after 5 years would the twins see themselves as the same age/height/weight etc. and the North Pole observer will see a 15 year old and a 10 year old similar looking boys standing next to each other??

[@DocSchuster]

39knights Accelerating reference frames are easy to detect - look for Newton's Laws not working. In this case, every object in the ship at 1/3 ly out would need a net force on itself just to stay in the dang ship. I heartily endorse doing this experiment, and I will wager whatever you like that the one who's out really far and in an accelerated reference frame ages less, according to good, old-fashioned special relativity. Call Elon Musk, and let's get this going!

[@kornelijekovac9793]

Problem: 5:18. Cody will not be 10 years old. It will just be from Zak's point of view that Cody should be 10 years old, but Cody will have aged 20 years because he's been away for 20 years from Cody's point of view.

[@wenniezhao9835]

If Z and C only compare them to each other, they can't tell which one is moving. But by using the same reference, the earth space-time coordinate system, Z and C will tell C is moving and Z is stationary.

[@matrikapoudel4022]

Yes the mistake is that the ship is turning back and when it turns back it has to accelerate and when it accelerates the inertial reference frame is changed into non inertial reference frame and special relativity breaks down.

[@allorgansnobody]

you mean to say that regular relativity breaks down this scenario is where things become special :)

[@seungjunbang7020]

+Jaime Cohen There is no regular relativity (there is general relativity which is a totally different idea to your "regular" relativity)... Einstein had two postulates for "special relativity" which are talked about in the first episode... The postulate broken down in this "paradox" is how the inertial reference frame is not kept due to the acceleration(deceleration is just negative acceleration) of the spaceship when turning back to Earth. This means that Cody knows he is "moving" so SPECIAL relativity falls for Cody. This means that he can't think that the Earth is moving but it is always going to be him that is moving, therefore the only case that works is when Cody only ages 10 years and Zack becomes 20.

[@thesid0797]

you make physics really interesting!! keep up the good word Doc

[@gonzalo653]

how far was the planet?

[@painfulearlobes6551]

Wait now I’m confused. How does flying clocks in the SR-71 disprove the paradox? From our (earthbound) perspective the flown clocks would indeed be behind relative to ours- but the goal is to disprove that from the pilots perspective (or anyone aboard the SR-71) earthbound clocks would be behind relative to the flown clocks (once landed). A proponent of the paradox could suggest something as stupidly amusing as multiple realities that take place after the experiment- one where, from the pilot’s perspective, she/he returns to earth experiencing a reality where they have aged more relative to the people on earth, and a reality where the scientists find that they have aged more relative to the pilot after her/his return. The paradox does not support that the clocks aboard the SR-71, when returned, should be the same-it supports that both perspectives (pilots/earthbound scientists) perceive each other’s clocks as, say, a minute behind- which is impossible. The SR-71 clocks seem to have shown that, at the least, one side of the coin is correct. To test the other, I thought one must literally be in the relatively “faster” reference frame (or else one would only be reinforcing what the paradox admits one’s reference frame should be). I thought the paradox was disproven because the pilot would not consistently perceive the time on earth as slower than her/his own due to deceleration (and perhaps other varying conditionals pending on the experiment). In this case, time might, in a sense, catch up and even speed up in accordance with the speed drop (on earth, as observed by the pilot). Did the SR-71 prove this momentary increase? I’m really confused now…

[@DocSchuster]

Painful Earlobes You have a good point. The true test would be to do EXACTLY the same experiment. For me, our SR-71 experiment confirms that accelerated reference frames do indeed experience distortions in time, and those distortions always make their time run slower. In my mind, this explains the paradox.

[@painfulearlobes6551]

Doc Schuster If by “explains the paradox” you mean “solves the paradox” then that is precisely what I am struggling to understand. To me, the paradox is similar to a riddle of reconciliation-i.e., if time is relative to motion, and motion is relative to some reference frame, shouldn’t both twins perceive each other as older than the other when they reconcile afterwards? If yes, is that not impossible? A solution to the paradox might be that only one reference frame is “really” accelerating (or moving), or, that time is not only relative to motion (and that is somehow significant to the particular experiment), or, time can actually increase during the moment of deceleration (the premise of many Sci-Fi films), or some other measure that causes asymmetry (relevant variance) between the two twins (reference frames). I thought that the paradox maintains that “accelerated reference frames do indeed experience distortions in time, and those distortions always make their time run slower (as observed by a slower reference frame- I think),” so the SR-71 experiment isn’t all that helpful to solving the paradox when it confirms this. The point of contention (or at least a point of contention) is whether it is accurate to describe both reference frames as “accelerating” and “decelerating.” In other words, the paradox is that both twins are equally correct in maintaining their perceptions as being older than the other - the SR-71 experiment seems to show that at least one of the twins is right, but not that the other is wrong.

[@zodiacfml]

The problem is the paradox as there is none. The only way to know which one is younger or older is comparing their clocks. If both twins left the earth on opposite directions at 0.25C and came back at the same time, they would have aged at the same rate despite their distance away from each other is 0.5C; they experienced the same amount of time dilation.

[@WideCuriosity]

Explaining what seems impossible is hardly worth a video for. It's too well known. This really needed a novel and easily understandable explanation on why reference frames can explain which guy is to be the one to have aged less and thus broken the expected symmetry. The explanations I've found so far seems to take one so far but still leave an amount of confusion preventing instinctively understanding what's happening outside of graphs & equations.

[@deathstouchoflife1275]

So that's why I'm so smart I was the slowest kid in my grade and still am the slowest to this day

[@eyemoksha]

(Edit: Just released that this video is 7 year old 😣) Hi Doc Schuster, I think it breaks 'relativity of simultaneity'. Am I correct? If no then What's the answer? Please share

[@grizzlyfauz84]

If light travels at a speed of c at any reference frame then what would our speed be if the reference frame is a traveling light? Will it be c, zero or something else?

[@DocSchuster]

This is an excellent question - one that led Einstein to develop Rel. in the first place.The trouble is that you can't ever have anything in that frame you're suggesting. And no observations can be made from it, because it doesn't experience time (it only experiences distance).But keep thinking like that, and you'll change the world. Go.

[@nadavdanieli]

Paradox arise for misrepresentation of the situation. Cody does not "see" Zac's clock slowing down, his far synchronized clocks do, and this goes to Zac too. At their own x=0 the clocks of the other actually move faster, when you change direction take the times at the same x=0 location. Whatever happen on the way out will reverse on the way in. An observer placed between them will always see their clocks are the same at his x=0, both on their way out and in, when they meet again there is no time difference. In this picture oi65.tinypic.com/14afsko.jpg, the number of light signals that are sent at the same time interval is equal equal to the number of signals received.

[@itc1509]

Cody accelerates to leave and to turn around and come back so his isn't an inertial frame of reference anymore.

[@sharang115]

If something travels at the speed of light ( or very very close to it).Then it would cross the length of the universe in a very very short period of time(due to length contraction and time dilation).So in case of photons which travel at a speed c, shouldn't they also do the same.But we know light from distant stars take millions of years to reach earth.

[@DocSchuster]

sharang chopra ...FROM YOUR PERSPECTIVE. Light does not experience time, Friend. Keep watching.

[@MysticMD]

I don't understand !!!!!!!1 why you leave us hanging!!!!!!!!! I understand every point that you made in the video... but who is actually younger when cody comes back É!!

[@aravindnarothe]

The question "Who actually is younger" doesn't makes sense in relativistic world. Both of them sees the other younger than himself. This is the point Einstein was trying to prove. Time is not absolute. It's relative to observer. You see the world from your perspective, So as I

[@DocSchuster]

aravind n Your statement is totally correct for two inertial reference frames. The twins can't even know who is younger as they zoom away from or toward one another. But when they do come back and are at rest relative to one another, they will agree that one twin is actually younger. Which one?

[@aravindnarothe]

Why do you say that, when twins finally meet they agree upon one's time? This means that one twin was wrong throughout the journey, which contradicts relativity

[@DocSchuster]

aravind n "...which contradicts relativity" is your only mistake. You missed one key statement when I defined special relativity. It changes EVERYTHING in this problem, and resolves the paradox. Good luck!

[@aravindnarothe]

Doc Schuster I had been behind this stuff for a couple of days.. I watched many videos and read some blogs which claims to solve Twin Paradox. But still I am not ready to digest any of those solutions :( The most important thing that all of them suggest is that, the twin that travels away from Earth will be younger. And the reason is asymmetry in calculations. And this asymmetry comes into picture due to the fact that, the traveller knows he's travelling due to acceleration and deceleration involved during the travel. I've different idea. Acceleration and declaration is involved at three points of the travel. Make the traveller sleep during this time, so that he never be able to distinguish if he's moving or the earth is moving. Calculate each others time during the rest of the journey. Now traveller would never know that he had really travelled. He can equally assume that the twin on earth has travelled. Now we have a complete symmetric scenario. What would be the outcome?

[@Gilmaris]

If Zach sees Cody's clock tick more slowly, what does Zach's clock look like to Cody? Ultimately, does it matter whether Cody _thinks_ that Zach's the one moving when it is in fact Cody? Sure, he can make the calculation, and he could do it right, but he'd still be wrong. If we postulated a third observer ("God sees all"), he would know which of them were moving, and could be making the correct calculations.

[@DocSchuster]

Gilmaris The same - slower. A principal declaration of special relativity is that both inertial frames are accurate.

[@Gilmaris]

Doc Schuster Even to a third observer who is in a separate location from both? To him, Zach will not be moving, but Cody will be.

[@DocSchuster]

Gilmaris Couldn't you get a FOURTH observer who is at rest relative to Cody? You're dancing around the actual problem. Look up what inertial frame means.

[@Gilmaris]

Doc Schuster That would mean the fourth observer was travelling parallell to Cody at the same speed, and started travelling at the exact same time, and accelerated at the exact same rate. A third observer is sufficient. Zach and Cody both start out at the same location, location A. The third observer is in position B. Once Cody starts moving, he is no longer in position A. But Zach is, and the observer is still in position B. So what does the observer see? Is not his frame of reference more accurate than Cody's? At any rate, the problem is so academical it throws all reason to the wind. First of all, Cody has to accelerate. This is something Cody would notice. And Zach knows he's not the one moving, because he's not accelerating (even though he is actually constantly accelerating due to being on a planet revolving around a sun). Moreover, Cody would be able to tell from celestial bodies that he is the one moving. But most importantly, the paradox includes Cody returning to earth. Suppose he is not returning. Suppose they start watching each other's clock when Cody is up to speed, as it were. And suppose the experiment ends once Cody has travelled a certain distance, with no change in speed or direction. Who, then, has aged the most? The answer to this cannot rely on _knowledge_. Even if Cody _thinks_ that Zach is the one moving - if that's not the case, then that's not the case. And what if the third observer, let's give him a name, Pete, is actually travelling himself, but at different speed and in a different direction. What will this do to each person's inertial frame of reference?

[@keldanreb]

If i had a space ship the size of earth,then zoomed off at 90c . Then real earth would be leaving me at the 90c,so when you say time slows down for moving people,what is it relative to. I don't get it.

[@DocSchuster]

The acceleration makes Cody age LESS (not more). The point of this video is that Cody's trip can no longer be understood through SPECIAL relativity. Post this question again on my General Relativity video, and I'll answer it! He he he.

[@karthikashanmugam6749]

so if one of twins go to the past and change things that happened in the past, will it be reflected to the other twin?the only difference between between the twins is the age?sorry this is a very dumb question.. I am not a physicist... anyone answer please...

[@sangeethadeepak6255]

U can't go to the past.... Only to the future

[@The_man_himself_67]

Heh. You really f*cked that up. Lol.

[@helloandyle]

All i think about listening to this lecture.. INTERSTELLAR :O

[@Advunt]

The problem is acceleration was left out of the equation? The rocket is accelerating and decelerating. And gravity has an effect on time dilation as well, but that is a whole different mess. Either way that is my guess. I'm still trying to figure this whole thing out!

[@DocSchuster]

Advent Yup! And PLEASE leave gravity for later. Good thinking!

[@mikegale9757]

The worldlines of the twins intersect that of the centre of mass at the start and end of the experiment so they have to agree on the elapsed time in that context. Furthermore, they move in opposite directions if they move at all so the centre of mass is always somewhere in between. The only way the twins can agree about the elapsed time in the centre of mass reference frame is if the centre of mass stays put. The worldline of either twin is a zigzag in that context so they both age less than an observer at the centre of mass. (See kzbin.info/www/bejne/gnzNknWGi9mpo9U.) How they age relative to one another depends on how fast they move relative to that 3rd observer: t1 - t2 = t0 * ( sqrt( c^2 - v1^2 ) - sqrt( c^2 - v2^2 ) )

[@arwaabougharib8698]

In the context of the twin paradox, why do we apply special rather than general relativity? According to general relativity, the twin on Earth should be younger since she is in a stronger gravitational field, while according to special relativity, it is the spaceship that must be accelerating as it turns around, hence, time runs slower in the accelerating frame and the twin who is on Earth should be older... The twin paradox is a very controversial issue and many theoretical physicists have diverged in their conclusions from the results obtained in this video. For example, Professor Mendel Sachs reasoned that the twins will have aged the same after the journey is over ( Link to article lt4tz7xl8k.search.serialssolutions.com/?ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info:sid/summon.serialssolutions.com&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The+twin+paradox+repudiated&rft.jtitle=Physics+Essays&rft.au=Harada%2C+Minoru&rft.date=2011-09-01&rft.pub=Physics+Essays+Publication&rft.issn=0836-1398&rft.volume=24&rft.issue=3&rft.spage=454&rft.externalDBID=n%2Fa&rft.externalDocID=268403444&paramdict=en-US) Dr Schuster .. My Brain Hurts !! please help : )

[@UnamazingMoi]

The one on Earth is 20 and the one on the rocket is 10 at the end of the story. The guy on Earth is right, since his frame of reference is inertial, whereas the frame of reference from the rocket is non-inertial, since he must accelerate to turn around to come back, either by making a circle or slowing down and then speeding up.

[@JamieTwells]

But what if they were both in rockets and set off in opposite directions, and both accelerated? What if the situation was completely symmetrical?

[@derekbauer7661]

***** Ah hah! That's exactly the point of this! When they are reunited, they are both the same age! This is because when the one twin leaves Earth, he has to fight against the gravitational field (accelerate against it, thus causing a time dilation). When he's out in space, the two twins are in fact different ages. However, when he comes back to Earth, he now has to de-accelerate, reversing the time dilation. And so, at the end of the day, they are both still the same age.

[@UnamazingMoi]

Mining With Derek You don't reverse time dilation. There is no such thing as "deceleration", there's only accelerating in different directions. Since the only velocity term in the time dilation formula is being squared, it removes the negative, thus making it essentially a scalar. Direction doesn't matter when discussing time dilation.

[@derekbauer7661]

Dexter Morgan I don't really understand what you are saying... how can you only accelerate? There would be no stopping then, right?

[@UnamazingMoi]

Mining With Derek If you are traveling and accelerating to the right, the way you slow down is by accelerating to the left. Acceleration is defined as *change* in velocity, not *increase* in velocity.

[@johnmccoy2119]

Relativity was violated, because for lack of a simpler term, equivalence is experienced by both observers but the outcome does not match Newtonian Mechanics

[@mfst100]

The first principle that was violated is when you wrote '5 years as seen by Zack', s(should be by Cody) and than there was even more confusion... So far I don't see the good explanation of this paradox on KZbin. Do the video again, please. Do not rush. And you can skip the equations Mr Doc.

[@mattacer1]

the guy in the rocket is actually younger because of acceleration he is not in an inertial system.

[@cm5754]

The issue in the paradox is that each twin says they were stationary, and hence had zero acceleration, while the other was moving.

[@manog8713]

You are thinking about acceleration, right? This is really not the way round the paradox. The situation is completely sysmmetrical and accleration should not be considered in inertial frames. If you take acceleation, then you are not allowed to use the assumptions of Special Relativity and the Lorents transformation. besides, the effect of short acceleration can be calculated which is actually minimal. This is a long story and the justification is a real mess.

[@JohnCurry1]

The situation is not symmetric because Cody has been accelerated and Zack has not. The two don't have identical histories.

[@cm5754]

But the paradox is that there is a simple coordinate transformation that swaps which twin was stationary and hence swaps which one was accelerated…

[@LukeBurgess3]

The paradox is not the problem... any brain dead person can tell you it takes acceleration to define who is actually doing the moving, this acceleration will be felt as gravity by Cody and thus he will know he is moving away from Zach. Zach will only feel the gravity of the planet and nothing more so he will know he is stationary... anyways, it take triplets to see the problem, one stationary the other two moving away from earth in opposite directions. We can call the new brother Jacob, and Zach still stays on the planet. Now, we know that Zach should see Jacob age in the same way as Cody... but, How could Cody and Jacob return with no aging relative to each-other?

[@mfst100]

What is so special about inertial frame of reference? Why does it make somebody age faster than in non-inertial frame of reference?

[@lutherschultz4725]

is it because in the twin's frame of reference, he sees earth travelling a longer distance due to lorentz contraction?

[@trapez77]

What if you watch 2 live streams of 2 clocks moving at different speeds? How could the length of the videos be the same, but still end with different times on the clock?

[@DocSchuster]

+trapez77 The length of video is your elapsed time. The clocks' displacement is the elapsed time for the other clocks.

[@trapez77]

+Doc Schuster but if your watching the livestream and observing both clocks tick at the same time, how can the hands still be in sync in the video, and not in reality? When the clock gets back to you, you will be watching a video of the past and it will no longer be live?

[@DocSchuster]

+trapez77 No, the hands are certainly not in sync. You always perceive that their time is going slower. Remember - their clock is in dramatically different places every time you see it. Wait a second - by livestream, do you mean that THEY film their clock and broadcast the video to you? Perhaps that's the misunderstanding we have. I'm not sure what the digitization packeting would do to the timing, but if they digitize each frame and send it to you, you won't get a frame from them every time you yourself would have recorded a frame of video using the same camera.

[@trapez77]

+Doc Schuster thats what i ment, so you would be seeing the video in slow motion?

[@DocSchuster]

+trapez77 Yes!

[@isaacpender]

I've been trying to get an answer to the question at the end of the video. Why does is cody actually 10 years younger when they both see each other's time moving slowly. Many say it is because of the acceleration when cody turns around, but that is irrelevant to special relativity, where it only includes uniform motion.

[@Arkalius80]

It's not irrelevant... the fact that one person accelerates means there are 3 reference frames, not just 2. The acceleration alters the traveler's time orientation.

[@isaacpender]

yeah but then why does the time travelling at constant velocity in the spaceship matter?

[@Arkalius80]

I'm not sure I understand your question...

[@isaacpender]

like if the twin in the spaceship only ages slower in reality only when he accelerates, then why does the time he travels at near light speed at constant velocity matter. He only accelerates for a split second when he turns around, so the 10 years he travelled at constant velocity should not matter (Obviously it does, but I'm trying to figure out why since people always say he accelerated when he turned around and that's why he is actually younger)

[@Arkalius80]

There are two ways of looking at it. From a purely special relativity perspective, his acceleration is what is called a Lorentz boost. It transforms his spacetime coordinates, altering his idea of "now". When he left Earth, his clock and his twin's were synced. Just before he accelerates, the Earth clock will be behind his due to time dilation. Buty, when he accelerates, his perspective of "now" changes such that the time on the Earth clock is now far ahead of his. As he heads home his clock catches up a bit since Earth's clock is slower, but it will still be ahead when he returns, leaving him younger. From a general relativity perspective, acceleration is equivalent to resisting a uniform gravitational field that is "pulling" everything in the universe in a particular direction. Time moves more slowly for things deeper into a gravity well, and sine he is much "deeper" in this apparent uniform gravity than Earth is, Earth's time ticks much faster than his during the acceleration, such that he'll be younger when he gets back.

[@shreyasbhat3957]

sooo...... what you mean is i will be experiencing time differently at the same moment , for different people , travelling at different speeds ??

[@DocSchuster]

You'll always experience time as you have been. Others may think your time is running slowly, and you may think the same thing of others.

[@1965ace]

Yes perception is not objective. Consider the earth was moving to the left in this illustration at .87c the entire time (no one would know) ........ Cody would initially experience twice the amount of time Zach was experiencing then turning around would never catch the earth but only match it's speed at .87c. But wait there is no measurement on the earth to deturmine it's velocity to begin with (that's true). We could measure earths velocity against other planets, stars and galaxies but that would only be an approximation relatavistic speeds would be more appearant (celestial events would appear to happen faster). The only objective method to tell is compairing clocks across the universe, the clock with the fastest rate is the one moving the slowest.

[@shreyasbhat3957]

and can you explain me the derivations for the formulae which you used in the video ??

[@DocSchuster]

Yes! Look for my relativity playlist. You jumped into the middle. There's a link to my video index on my channel page, too.

[@jackl1750]

In the diagram it's said that Zach watches Cody move right for 5 years. Shouldn't it be 10 years?

[@jackl1750]

Nvm someone already addressed this. Thanks for the videos but this one isn't that helpful and confusing in a sense.

[@DocSchuster]

Aflac Sherry Thanks for the feedback. I'll put this on my list to remake.

[@ouroborosnagyok9306]

0:38 ok so basically.....moving people (like the people who work for U-Haul) actually live longer??

[@nadirarfi2342]

the suite life of zack and cody haha

[@aravindnarothe]

I understand the paradox. But one doubt. Why do we measure time using light? What if the world was blind? I guess we still would experience time. I believe that time is not something which has to be measured on the basis of ticks of light. It's more subtle and real.

[@DocSchuster]

aravind n I suppose, with advanced technology in a blind civilization, you could measure time using gravity waves! I think you'd get the same result. Good point, though. Light (and everything else that goes that fast) is special because it doesn't experience time.

[@NihongoWakannai]

you dont need to be able to see light to be able to detect it. we can detect electromagnetic radiation of higher and lower frequency than what is visible to us.

[@gustavobagu7156]

Doc Schuster: I think that DELTA TEE NAUGHT has to be Cody´s time acording to his spacecraft bound clock... and not Zach´s time. Don´t you think?

[@arunredddy]

I think einstein was wrong in this paradox....because zack and cody have present events according to their frame of references.....and zack would never be able to see the cody clock or the light beam when he travels @speed of light...because the light can never reach zack to watch....and when the cody is in his present .....he will see normally according to his frame of reference....and both the times are equal to delta t and the thingwe observe the things as past and prrsent things with relative to each other....

[@arunredddy]

Both the cases light travels in the staright line so t is 2d / t.....no need ofbpythogrean equatiin because when cody can never see zack because the zacks present event of the experiment is codys past event....which he can never see the zack light as he is travelling in future with reference to the zack.....both are in present according to their frame of references...and zack will see the light travelling in straight line but after the event is finished.....and i hope both will be of same age when cody comes back!!!!!

[@jimdogma1537]

Do you ever address what the paradox is in a later video. What do you mean the answer is hidden, can you find it? This isn't a homework problem. Do you know it or are you playing some kind of joke?

[@AnimeAuraArtistry1]

i actually stopped the video to see SR-71 XD

[@mathveeresh168]

It's not the acceleration

[@B--Roll]

No paradox... the time dilation happens to the one that is moving at close to light not the observer of light, Looking at the sun does not dilate time for observers on earth but the light particles themselves certainly exist in a timeless dimension at light speed. Twin A moving at light gets the time dilation... Twin B moving at solar system speed has a far less time dilation. Now we think even the speed of light may have been different in the early ether too, so would be time to an observer back then or even now in the full spectrum that echoes from back close to the beginning.

[@SlurpKing100]

The thing is when twin B (the on a space ship) is looking at you he's seing you move away and back to him. And for him looks like twin A's time gets dilated. Time dilation doesn't happen to just anyone thats moving cause in the real world you can never know who is moving and who is stationary, that is basic relativity. example: If you are sitting in a car that's moving you will think you are stationary and the ground is moving, but for someone who is standing at the ground they will see you and the car moving. It all depends on what frame of reference you're observing.

[@SlurpKing100]

Also if you want a mathematical explanation: The equation for time dilation is t'=t/[square root of]1-v^2/c^2[square root of]. Where t is the time elapsed for a stationary observer and t' is the time elapsed for a moving observer. From the stationary observer's perspective the moving observer's time is slower. But if you apply this equation to the moving observer he is no longer moving and the observer that was stationary is now moving. Another way to think of it is that YOU will always experience a "normal" time no matter if you're moving or not. But the ones that are looking at you will see your time moving slower when you are moving, while simultaneously you wil see THEIR time moving slower.

FYI, critical explanation of the paradox of Langevin's twins on kzbin.info/www/bejne/rKPYdH13it18Zq8 (English subtitles available)

[@vinayn9110]

Is that why athletes look younger? i.e. they move a lot and benefit from time dilation?

[@DocSchuster]

Ha!

[@abidzoardar]

Yes because athletes moves at the speed of the light ....

[@mgominasian9206]

but when you made a substitution in the equation delta T=2*delta T0 10=2*20 how is that possible

[@rhythemh8635]

You got it all wrong idiot

[@nickbjergjensen1182]

are you actually counting zacks time to go backward? , because time just go 1 way bro. otherwise, I see no dilemma or paradox :)

[@walter_mayer]

I can't hear any longer this argumentation with the inertial system. Let us assume the rocket starts and accelerate always with 1g. So both have the same gravity. After about 11 months the rocket will change the acceleration to -1g and after further 22 months switch back to 1g. So after 44 months he will come back. He have experienced always 1g gravity. And we now that 0g (e.g. about 1min) while switching over have no remarkable effect on time. Both will see the other one younger! I do not see a problem. If you look someone fare away from you he looks smaller. Nobody assumes that the other one will see you bigger. We are in time-space - why should anything different? P.S. If you now come with the argumentation at earth the acceleration did not switch. No problem - assume both are sitting in rockets and do the same, including the g-switching.

[@allorgansnobody]

+Walter Mayer The example of the people looking at each other doesn't hold up. In that example, neither parties are moving anyways. The point is that one can tell when oneself is accelerating or decelerating, but one can't tell if one is moving if there is no acceleration. Look at it like this, while you are in a plane in flight, the acceleration and deceleration is barely noticeable, if you close your eyes and forget where you are you can not tell that you are moving at 700+ km/s. However, if you are in a car that is rapidly braking, and is therefore decelerating, one within the car could easily tell that they are decelerating. In the same way, the rocket in the story has to start at 0, and reach 87% the speed of light, and then return to 0, which mathematically necessitates acceleration and deceleration, and therefore causes there to be a distinct difference between the perspective of the planet and the rocket, there are no jump asymptotes in the real world.

[@walter_mayer]

+Jaime Cohen It is the basic idea of general relativity, that acceleration and gravitation is equal. If you sitting in a lift, you can't distinguish, whether your lift is on earth (not moving) or somewhere in the space and accelerating with 1g. You also cannot distinguish, whether you are constantly moving in the space without any gravitation or whether your lift is in free fall situation to the earth or other gravitation field. So the time effect must be the same in both situations, otherwise you can distinguish whether your lift is in a gravitation field or in the space and accelerating with 1g. So what remain is the effect, switching from 1g to 0g to -1g. We know from space flight and calculation, that switching even for days and month the switch to 0g could be neglected. It could be only measured with very precise atomic clocks. So the only significant time effect result from speed. And this effect is for both equal. And as I already stated, modify the experiment a little. Let both twins start the space flight with opposite direction. Switch over to the other acceleration in both rockets to return to earth. Then the twin paradox experiment is complete symmetric. So each will see the other younger.

[@Fransamsterdam]

What's wrong is the statement that explanations can be found easily on the internet. Most of them say that the difference in age is caused by an asymmetry, because one person accelerated and changed reference frame a couple of times, but that makes no sense to me. If both persons make a journey, with the same accelerations and changes of reference frame, but they would travel at a constant speed for different periods, there would be no asymmetry as mentioned, but there would be a difference in age.

[@DocSchuster]

+Fransamsterdam Eh? If they have [opposite] accelerations at start and stop, they will travel at constant speed for /identical/ time periods in order to meet again.

[@Fransamsterdam]

Doc Schuster They travel not for identical time periods. One can travel to a star at 5 lightyear from earth, the other one to a star at 10 lightyears from earth. If you like the stars can be in the same direction. They accelerate at same time to same speed, only turning around and decelerating will happen later for the other. When they return at earth, there will be a difference in age.

[@DocSchuster]

+Fransamsterdam Sure - this is no paradox, though, since they actually did different things. You need triplets now. But all three will be different ages when they return to earf. I do not understand your concern - sorry!

[@walter_mayer]

+Doc Schuster Fransamsterdam stated to make the thought experiment symmetric. Both twin will start in opposite directions with same acceleration, same constant high speed phase, same turn acceleration, same constant speed phase, same braking acceleration to return on earth. Everything is symmetric. So each of the twins must see the other younger.

[@Fransamsterdam]

+Walter Mayer Not exactly Walter. They travel - in my example - in the same direction. The only difference is the time they travel at high speed. Then everything is symmetric, except the time they travel, but during that time, there is no acceleration or change of reference frame, so the difference in age - which there will be in my example - can not be explained by the difference in acceleration or changing reference frames. The only 'assymetry' is in the length of the time traveling at constant high speed, so that must cause the difference in age, but then the paradox rises again, because when traveling at high speed, why should it matter who is taveling and who not?

[@ouroborosnagyok9306]

MUTANT SPACE FISH

[@imissmyoldpassword]

Its because their tlocks would cik slowly!

[@sharongazibo969]

Hey I love this guy

[@moiquiregardevideo]

Christian Gingras 5 months ago Nice attempt to explain the paradox. Here is a simpler explanation: When the Sarah is flying away from Earth at 95% the speed of light, the radio communication is impaired because of a Doppler shift. Both sister need to tune their 1 GHz frequency to 50 MHz, which electrical engineers call carrier frequency. The AM or FM modulated signal, a slower wave which modify slightly the carrier frequency amplitude or frequency is equally slower. All embedded binary code are also streaming 20 times slower. The decoded voice of Sarah is deeper, like playing a vinyl disc or magnetic cassette in slow motion and the video are almost still pictures. A year later, Sarah turn around and come back toward Earth at 95% the speed of light, the following happen: That day, one year after their separation, Alice on Earth keep receiving the slow stream of radio at 50 MHz. She just received the video from Sarah telling how boring it is now, after 2 weeks of travel. She think her sister is crazy, talking about 2 weeks when in reality she his gone for a year and she is supposed to turn around now. Sarah also receive old news from her sister on Earth. She see the video telling her that she already miss her after two weeks of separation. However, the radio is fucked up because Sarah at the switch frequency from 50 MHz (for the 1 GHz carrier frequency) to 20 GHz. Also, the voice sound like chip monks and the videos are 20 times too fast. As the time pass between 12 month and 24 month of the total duration, the video that Sarah receive from Alice catch-up with the real time. Everything synchronize just right so that the last day of this 2 years voyage, Sarah can see a video of her sister recorded only 20 days earlier. For Alice, the second year events are a little more complicated to explain. She keep receiving outdated video on the radio station tuned at 50 MHz. Suddenly, 2 weeks before the end of the 2 years trip, the frequency jump from 50 MHz to 20 GHz. The video from Sarah describe that she now prepare to turn around. Alice think that she is crazy to announce that after 23.5 months. Then, during these last 2 weeks, Alice receive all the videos from Sarah describing that entire year where she is flying back to Earth. Finally, both sisters re-unite and they both aged by exactly 2 years. End of paradox.

[@rayzimmermin]

the problem with the twin paradox is one our concept is based off of clacks that are effected by movement and gravity giving a false perception of time what time is we can brake the twin paradox with an out side observer do to the fact the twin paradox relays on the twins prospective of reality what would a third party see them age differently no thy would see them age the same only the clocks would be moving differently do to how the clocks work their is a grater distance between ticks of the clock moving so to an outside observer the clock would be moving slower but the person inside would age at the same rate as the one on earth also the SR-71 black bird and satellites experiments do not prove time dilation as thy all were one way trips and not return trips what i mean is the SR-71 took off flew around the world and landed that is not travailing out and back and satellites do to how thy work move in only one direction the atomic clock is what is effected by velocity and gravity not time its self hears a better twin paradox devoid of the atomic clocks take a decaying radio active mass split it in two put on have on the rocket keep the other half on earth fire the rocket at your 98% speed of light for half its decay and bring it back so just as it hit earth its fully decayed will it decay after the one left on earth NO because the rate of radio active decay is constant

[@alchemy1]

No, you just goofed right from the start. The faster I go having constant velociy, the slower your time goes, not mind. I have every right to stay I am stationary and it is you that is moving. That is your teaching. You are confused big time. That is what relativity is all about in the first place. No matter what is up, you are the staionary one. You are always at rest in space. Moving or not.

[@animoshho]

If your SR-71 airplane was going faster than the speed of sound, how did the atomic clock work properly?

[@yassinboykobaan417]

it was used with photons

[@rayzimmermin]

that ware the twin paradox comes from how clocks work not how time works speed effects how we measure time not actual time

[@weihanlim8368]

I would suggest speaking slower, in order to be understood more clearly.

[@awsomeabacus9674]

yo nose is always wich you!

[@manstett7066]

you should teach chemistry LOL

[@laveenbagai6327]

If twin paradox is proved practically it will be the biggest success of science but I have lot of bit of questions. Firstly if twin paradox is true then travelling in a car with speed 100 km/hr would also suffer twin paradox but its not when we step out of the car then the person that has travelled some distance in car and the observer will have same time. Ok this can be true some of you guys will say that in this case speed is very less and it suffers negligible twin paradox. But lets take large distance then it suffers very large twin paradox but it is only a assumption yet not proved, it is actually not possible to travel with the speed of light. According to me time is nothing but a single physical quantity which does not even vary (slows down or become fast) it is all constant means that 1 sec will be over in only and only 1 sec not less or more. If it is not then spaceshuttle going into space would reach more fastly according to the time reference than the estimated time by scientists. If twin paradox is true then what actually is time. Is it simply a physical quantity or something else. I think time is not absolute according to reference but constant or fixed according to speed velocity of the moving object. Time does not vary the thing vary during movement is speed or velocity.

[@WaiteDavidMSPhysics]

To many childish antics.