Twin paradox: the real explanation 

Well, I find the video has a long introduction and then finishes off a bit too short with the conclusion that the moving person exists in two reference frames, period. That part, the meat of the paradox, should have been better explained.

Please make a sequel, the "conclusion" needs more explanation.

Like others here, I don't see the explanation. I hear "two frames of reference" but I can't connect that observation to an explanation I can grasp. It's like you ran out of time.

I'm sorry but you went all detail with the easy and well understood part, explaining it like we would to a 5th grader, and then just conclude in literally 5 seconds that since the observers B and C are not in one single reference frame (wich could have been explained as well as the rest was) this is the proof for the paradox not being a paradox. While I'm sure this is correct, and not wanting to tell you how to make your videos, this last part ,with no explanation at all to support or motivate your conclusion, didn't really prove anything to me. Still, it did provide for a starting point for me to dwelve deeper into, so thanks for that.

I'm having a serious problem with this explanation. I get the idea that it's a question of which clock you're using as a reference but nothing shown shows why Ron's choice of his clock as the 'stationary' one is not the same as Don choosing his clock as the 'stationary' one. It's like somewhere in there, there's an assumption of which one is really stationary when in fact, once you exclude acceleration as a factor (which you do), then neither is a preferred frame. Even though it looks like it's solved the mystery - throughout the entire discussion, A is referred to as being 'the stationary person'.. but that's literally the thing we're trying not to say. Take all the math done and flip the contexts and they apply equally well and give exactly the same results relative to each viewer, except you're swapping A and B. That's the problem with this video - it shows the math from the 'stationary' person's view - but not from the 'moving' person's view in the perspective of his being the stationary person. Oh.. one other thought. In another video, you explain that the reason there is time dilation at all is a consequence of the fact that we're *always* travelling at the speed of light. Assuming we're just talking about one spatial axis, x, and one temporal axis, t - the vector must always be a unit vector... so at rest, it points entirely along the time axis and represents 1 second per second. As you change velocities (and I'm avoid saying acceleration intentionally because it's the velocity that causes it, not the acceleration) the unit vector rotates until you hit the speed of light where all of the vector lies in the x axis and there's no vector in t - ie no time movement. It seems like you're offering two different explanations for dilation. Keep in mind, I'm not saying you're wrong - you know way more than I could hope to about the subject.. I'm just suggesting that this explanation could be better.

I'm 67 and retired, but WHY could I not have had a Prof like you in University. You make complex things so understandably easy. Please keep teaching our hungry minds. Thank you Sir ! ! !

I believe that there is an error in 10:25. According to observe C's perspective: the x co-ordinate (position) of event 1 would be -2yl, the x co-ordinate (length) of event 2 would be 0 and the x co-ordinate (length) of event 3 would be again 0. This is because the events' positions are relative to the perspective of C. It can also be supported by the x co-ordinates of the 3 events according to observer A and B's perspective since in the video the x co-ordinates of both perspectives are relative to the observer (i.e. for observer B event 2's x co-ordinate is considered to be 0 as the observer B and event 2 are on the same position). According to example I wrote in parenthesis, the x co-ordinate of event 2 for observer c would also be 0 as observer B and C are on the same position as well as event 2. However, this does not effect the conclusion reached. Please reply me either you believe I am right or explain my mistake.

I found this version to be better than the version without equations. It would have been more clear if Dr. Lincoln had explained what he meant by "the moving observers existed in two [frames of reference]". When he said that, he meant that the moving observers existed in two _separate_ frames of reference. Thus, he debunks the notion that the acceleration explanation for earthbound Don being older than astronaut Ron. So, the twin paradox isn't a paradox. It's just a conundrum ... and the conundrum isn't explained by acceleration, but by the Lorenz transform equations.

Sorry but you haven't done any actual explaining. Yes, you've set up a thought experiment with a departing and returning frame of reference that does without acceleration. You then arrive around 11:59 at "Duration(moving) = Duration(stationary)/gamma". But this is equally "paradoxical" as the original problem, because "moving" and "stationary" are still relative. You would actually need to show explicitly that the results are consistent if B or C were considered stationary AND independent of which clocks you use to measure the time between the different events. I'm sure it'll all work out but it seems awfully complex (involving relativity of simultaneity) and is definitely not obvious.

Some people just have a knack at breaking down complex problems to smaller, more complex problems that are even harder to understand.

I still don't get it. What did he mean by "Observer A exists in only one reference frame but observers B and C exist in 2"?

"When we start the experiment, all 3 observers start a stopwatch." This sentence contains the idea of "simultaneously". Problem is, simultaneous in whose reference frame?

Excellent explanation! I noticed there is a mistake for the perspective of the referential frame of observer "C" for event II, where instead of position γL should be 2γl. After struggling with the problem, I saw you already have made the correction. I think it is important to highlight that the origin of three frames started together at the event I. There is an asymmetry to explain the paradox. While observer "A" measures the difference between events in two clocks at rest where these events happened (B-A) and (C-B), each one of the observers "B" and "C" measures the interval of time on their own clocks attached with their bodies. The second intervals are proper times, related to the interval of time measured by "A" for dilation time expression: each time interval for A equals γ multiplied by each proper time interval .for B and C. If we begin with the interval measured by observer "A", we have to subtract the quantity of xv/c² for event B and add the quantity xv/c² for event C because the clocks are advanced in the direction of motion and delayed in the opposite direction by these terms according to relativity of simultaneity . After that, we have the interval of time passed in only one clock in the frame of observer "A" and we must multiply it by γ to obtain the interval for observers "B" and "C". In other words, the origin of asymmetry is the relativity of simultaneity expressed in Lorentz Transformation. Each one observer can claim the other clock is slower, and each one observer can consider moving in the direction of future of the other reference frame as expected by symmetry.

As a teacher of A-level Physics I found this video interesting, especially as the textbook we supply to our students gives the acceleration & deceleration solution. A past exam question (AQA exam board) explained it by saying the rocket twin was in a non-inertial frame of reference.

'Physics is everything', it truly is. (Edit) We shall miss you Dr Hawking. 18-03-14, a triumph we had you so long and sad loss.

Since A, B and C were not accelerating, they were moving (parting away or coming closer) steadily with respect to one another by exactly the same amount. Since there is no "Stationary" frame of reference, all three would think that other two inertially moving persons are aging younger by exactly the same amount(e.g. 6 years). A would think B and C are younger by 6 year, B will think A and C are younger by 6 years, and C would think A an B are younger by 6 year. It is understandable why the presenter abruptly cut off the video by just mentioning: it is because to ONE frame vs TWO or THREE frames -- instead of steadfastly reasoning why A would grow older by 6 years from others perspective while others would remain younger despite same relative motion! He could have plugged numbers in those equations that are 100% same for all three and prove why just one of those three symmetrical equations would magically yield no time dilation!

The end of the video was the most critical part to helping people understand why the twin paradox is not a paradox. In my opinion, you failed that task. You hinted at the answer, but you did not clearly spell it out for people who do not understand. (Also, as I understand it, you synthetically created a jump discontinuity, which is equivalent to an "instantaneous" "infinite" acceleration. If true, the example fails to illustrate your point.) At any rate, the animations and video editing were boss.

I may have missed something here, but in the (x,t) coords for event II for observers B and C there seems to be an inconsistency. Specifically, the location (x) for B is given as 0, but for C is yL (I use y for gamma so it is easier to type). It seems to me that B should be -yL. If not, then C should also be 0, not yL.

This is GENIUS! It's like I have just had my decade-long storage of nagging thoughts+lingering questions+half-baked answers suddenly decluttered in 13 mins. Dr Lincoln, you totally rock like the new opening background music of this series. :)

A crucial point in the derivation is that the vx/c2 term in the Lorentz transformation expresses the effect of relativity of simultaneity. In C's frame of reference, the now-slice (the space-time points corresponding to t_C=0) is tilted such that it intercepts A's position at a *future* moment. A sees B's and C's clock time dilated by the same gamma factor as B and C see A's clock (total symmetry here), but when C starts moving towards A, C's "now" already corresponds to A's future (which is only possible when you compare times at different locations, a point Don Lincoln mentioned). That's why A sees more time passing as C crosses A than it took B to meet C halfway and C to reach A.

That doesn't make any sense. Although I'm willing to admit to being wrong, all observers should exist for everyone else and everyone can measure everyone moving. I'm willing to admit to not getting it, but it doesn't prove it to me. Maybe it's because I'm a humanities guy.

I sort of "get" this, but I also agree with brixomatic about "long introduction" and "bit too short with the conclusion". Do another video please to follow up this one! Three specific comments on this video: (1) I would like to see some sort of comparison of what each of the observers (A, B and C) experience, as I would like to see everything being consistent for observers when they are momentarily at the same point, 1 and 2. (2)I am slightly concerned about how the points 1, 2 and 3 are observed by ANY observer. Is it required that there is a NOW point for 1, 2 and 3 (in at least some observers view) when this all starts? Perhaps, if so, the NOW, or "start time" at 1, 2 and 3 can be called by "you", the passive 4th observer of this situation, in the same inertial frame as 1, 2 and 3. However, for that to be the case 1, 2 and 3 would have to be equidistant from you - and that puts them on a spherical surface. That means that B and C are accelerating when they are moving! (Although I can see the "local" time at location 2 could be irrelevant, in which case it can be on a straight line between 1 and 3.) (3)This video explanation shows that acceleration is not required to resolve the theoretical paradox but it does not mention any additional effect that acceleration might have should it occur. In a real twin paradox experiment, acceleration would have to occur. And, since acceleration is equivalent to a gravitational field (in which clocks run slow), additional effects of acceleration in a real situation should at least get a mention in this video.

To Dr. Don Lincoln and Fermilab: I like that you have experimented with a changed scenario to try to finally end the twin paradox of the special theory of relativity. But I got completely lost at the end of the video. I think that such an important theory experiment should be well worth the added time to end the video with a detailed explanation. My theory, matter theory, explains the same observables as the special theory of relativity, but differently, and without any paradoxes. If you are interested, you can view my video, “You’ve Learned Relativity Theory”, which challenges anyone’s understanding of relativity theory. I am curious to learn what you think of this video. You can find my videos using the search keywords: matter theory marostica.

I agree with all comments about how the crucial thing was done with in 10 secs. A full video about that would be more than motivated. I am very fond of all the Fermi lab videos including this one. I have tried so hard to understand this. Here is a triplet scenario A, B and C sit in a rocket each. At some moment B and C sets of to Alpha Centurion at 0.999c. At Alpha Centurion C accelerates backwards and stops on the planet. A calculates a lower timespeed for B & C when they set of. B calculates a lower timespeed for C than his own at Alpha Centurion. Since A and C are at constant distance A = C (timespeeds) but at the same time A > B > C. Please help.

Two questions then. 1) What part of the equation dealt with the delay of causality (light) it takes to get from 2l to person A? 2) You said person A only has one reference frame. However, In the twin paradox don was on a planet. Which is moving there for he also has multiple frames of reference. In fact. If everything is retaliative then counting the frames of reference is a paradox as they can be flipped. Inertia is still the only thing that separates them irrespective if you can work it out after the change in velocity or not. What have I missed? Example of my thinking based on your experiment. Let's slow things down to very (VERY) small numbers. put the two in cars going 100km/h. It was the previous acceleration that changed person c to 100km/h. So he is the one changing frames. You can see it based on the 100km/h but it's still the acceleration that caused it.

This has generated a massive amount of confusion. I think you need to use space-time diagrams.

I don't get how is it possible that we have one non-moving observer and two moving observers. Aren't all observers non-moving (according to themselves, of course) by definition? Considering B and C as moving isn't in fact still viewing the situation only from A's perspective? And how is it justified, considering that we have to prove that «Ron is younger» with every system of reference? So, for A, the velocities of A, B and C are: 0, v, -v; for B, they are: -v, 0, -2v; and for C: v, 2v, 0. Therefore, the order of the magnitude also changes: A: a

Thank you for answering my statement from your last video. You really cleared up my question of 'whom is stationary'. Absolutely BEAUTIFUL!!!

The original version of the experiment involves only 2 observers, in the explanation it involves 3 observers. Observers B and C see a shorter distance due to Lorentz contraction of length. But for the original version of the paradox, Ron and Don started and ended in the same inertial frame (one can forget about the earth which confuses the issue as it creates a non-inertial frame), it seems that the explanation does not deal with the original paradox. (Sorry, I am not a professional physicist.)

Nice video, but it seems that the resolution of this paradox still requires acceleration. Without acceleration, each twin will perceive the other as younger; the resolution requires a real comparison, and you at least need one of them to accelerate to the frame of the other in order to do that - no matter how many twins you have.

As a retired engineer and a wantabe physicist I love watching these videos. As a engineer I was typically assigned tasks that ultimately required a number. And if I was lucky I would find an equation (generated by some one much smarter than myself) that I could use to produce that number. So I am not sure why Dr Lincoln is reluctant to show equations. I am going to try and work through the math for this twin paradox. It might be nice if Dr. Lincoln worked a few specific examples or perhaps pose problem and for us to solve and give the answer in the next video.

This is excellent Don. Once again you have nicely simplified what normally confuses

I really like how you match your t-shirts with the video content 😃😃

Splitting Ron into B and C to get rid of accellerations could have been mentioned more explicitly, Still a neat explanation!

I have heard of the twin paradox a million times and only this video has ever made me see why it is both a paradox and not one. I don't think that has ever been properly explained to me before. Thank you.

Good explanation. Some side notes: If observer A is truly stationary, the observers B and C clocks will show the same interval times. However, if A is moving, then the intervals shown on observer B & C clocks will be different by an amount dependent on the absolute speed of A. This provides a theoretical means of determining absolute velocity for any observer. This too shows there is no paradox. While each observer has a self-consistent relativistic frame of reference and can locally consider that he is stationary within that frame of reference, comparing the clock intervals from A, B, & C can reveal which one is moving slowest, or not at all, from a hypothetical absolute frame of “stationary”. Of course, the precision of the clocks and measured speeds would be essential to determining that “absolute” reference frame with precision.

I’d like to see you do a video that incorporates the apparent simultaneity into resolving this paradox. As you change frames of reference, what is considered “now” changes. In imagining how the two twins perceive the flow of time, it’s like when the moving twin turns around, his “now” for the other twin changes. At a constant velocity, both would see their own “now” going further into the other’s past. When the one turns around the frame of reference changes so much that the moving twin see’s the apparent “now” jump so far into the other’s future that he can still see the other aging slower with time dilation during the entire trip, but arrives back home finding the stationary twin has aged considerably more than himself. Like Brian Greene talks about “now slices” in this clip: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-MO_Q_f1WgQI.html

I found both of Dr. Lincoln’s clips on this subject helpful. His thought experiment is not quite the same as the traveling twins thought experiment, but his experiment is successful in its own right in showing that acceleration is not key to resolving the twins paradox. For me, the essential point is this. The experiences of the two twins are not equivalent, because one involves motion of the twin with respect to his cosmic (space time) background, and the other does not. You can argue that, from his point of view, the spaceship twin has remained motionless while the Earth, and indeed the entire cosmos surrounding the Earth, have rushed away and back again. But in that scenario, from the point of view of the spaceship twin, the earthbound twin is moving along with his cosmic background; he is not moving WITHIN it. In contrast, from the point of view of the earthbound twin, the spaceship twin is moving within his cosmic background, with corresponding time dilation effects. That, I think, is the essential point. The seeming “paradox” arises because it is difficult for us to set up and explain the different frames of reference involved and how they relate to each other.

Help me out here. What are the two reference frames he is referring to at the end? A stationary one and a moving one?

I so wish you had said what I was thinking, that "Ron would truly only be four months older than when he left, while his twin brother - born at the exact same time back here on earth - would be nearly a decade older."

PhysicsGirl also has a great video about it, which is less deep, but more understandable for casuals.

It appears it wasnt just me left thinking 'but... acceleration is what changes your reference frame. So isnt this rather semantic?' but Im inclined to believe that when an experts explanation doesnt add up to me that I must be missing something. So I was considering the scenario of the twins being in a small spherical universe where one starts off and arrives back by going all the way round that universe without accelerating. Im not sure how difficult a problem that would be to solve, if it needs some heady general relativity or not, but perhaps in this case and other parts of general relativity it could make for a more substantive distinction between the two ways of thinking about this? Edit: I wouldnt mind hearing other possible suggestions. I have to say Im kind of confused by what incite hes really getting at here.

Some stuff are real hard to grasp yet i'm always coming backs for this guy because the way he speaks is just soothing enough to calm the anxiety i get from not understanding shit.

The acceleration explanation is IMHO the best one. The heart of paradox is that both twins can claim to be stationary and hence after the journey both can claim to be the older (or younger) one since according to relativity you can't decide who was moving and who wasn't. However this is not true. The acceleration breaks the symmetry of the problem. So the argument is not that the acceleration causes you to age more slowly but that it prevents one of them to claim to be stationary.

This was a bid hard to understand. The best explanation I ever heard was in the video "Raumzeitdiagramme und Zwillingsparadoxon • Aristoteles ⯈ Stringtheorie (16) | Josef M. Gaßner" (german) using Minkowski diagrams. Especially about the 26:00 mark was the breakthrough for me. Its totally obvious seeing this. Good video however, as always :)

How do they synchronize to start moving at the same time? Send a lightbeam as signal?

Thanks for doing another video explaining it with more detail.

THANK YOU! I'm so glad that someone finally stated this clearly. I've heard SO MANY people who do not really understand the "Paradox" part of this whole thing. It took me a while to understand it myself because of the horrible explanations that have been given...

Gonna have to study this video for a while, but gaining clarity about the "paradox" will be more than worth the effort! Thanks, Don!!!

How do you get them (A,B,C) to all start stopwatches at the same time?

At 5:32, the equations are ambiguous, without clear specification of the (x2,t2) and (x1,t1) coordinates. The Lorentz transform equations are often written with a - sign inside the bracket where (x2,t2) is the coordinate of an event occurring in an initially co-aligned system moving at constant velocity, relative to another "fixed" observer who logs (x1,t1) for the same event. It's OK to downplay the math for such a wide audience but not OK to the point of spawning confusion. Physics is not pure algebra - the symbols all have physical meaning! Having criticized this omission, I still do appreciate the intuitive explanation of the twin non-paradox using A, B, and C observers.

A point of possible confusion with this is at 8:07 where the statement is made that you can work out how you can get from 1 to 2 and back to 1 again without any acceleration. This is true for non-massive quantities, and it actually would take an infinite, impossible acceleration at position 2 to accomplish this with anything that has mass. You have shown that you can get information from 1 to 2 and back again this way, but not an observer or clock. If you compare the clocks of observers B and C and the "end" of the experiment, there is no difference. This example should be re-presented in a physically realistic point of view from observers starting from a common space-time point. Mixing observers that are in different frames from the start might create confusion and is not the essence of twin "paradox" since the starting point has two opposing frames that are not twins.

A perfectly symmetric scenario is described? B and C are absolutely symmetric. That being said, I understand it all and it doesn't resolve the twin paradox. You have to incorporate the asymmetry, and it is due to acceleration. Acceleration is outside the scope of special relativity and violates the assumptions of both SR and the Lorentz transformations. The twin that experiences acceleration is not even remotely allowed to say she's stationary within the context of SR or Lorentz. This is a part of the assumptions of the theory. You can pseudo-analyze non-inertial frames within the context of SR, but it is a logical violation of assumption. I of course follow your arguments, but they are mathematically, formally inconsistent when applied to the departing and returning twin. A better resolution is required. In the purely SR case, "outliving your enemies" can be achieved by relative velocity, but you have to have differential acceleration to get there and back. There is no denying that. To say that it is all velocity is denying the derivative. All things considered, this is an excellent video and among the best presentations on this topic I've seen. The bottom line is that if a departing and returning traveler and twin experience different accelerations, they will have different times upon reuniting. If they experience identical accelerations, well, they will have identical times. This post will likely be deleted by remote observer with faster clock, but I encourage you to read before.

(1) I thought an event was a point in spacetime. But your Event I for A and B is located at a different point in space than Event I for C. (2) If instead of a thought experiment you tried to carry out this experiment for real, how would you do it without accelerations? How do B and C reach v and -v in the first place. (3) It is a paradox. It's not a contradiction. It has a rational explanation. But it is still paradoxical. (4) The maths works out, but you are still not explaining what it is that causes the aging of one twin to slow down. I'm still left with the suspicion that the initial acceleration shifts the travelling twin into another timeframe. I'm not saying that the dilation occurs during the acceleration, but without any acceleration there would be no time dilation. From this it seems to follow that acceleration is central to the effect.

First error is : x'=g(x+vt). The correct one is x'=g(x-vt), so is for t'=g(t-vx/c^2)

Okay, I think the proper take on this, this lack of symmetry, is that the distance from A to the "goal" (space station or star) is different for the A, B, and C observers. Since A and the goal are traveling at the same speed (more or less) there is no Lorentz contraction involved. A sees the "proper" length. But since B and C are moving with respect to A *and* the goal they see the distance between A and the goal as shortened. A, B, and C all agree on the speed that B and C are moving with respect to A and the goal. This *must* mean that B and C will take less time to travel the shorter distance than A experiences back on Earth. It's that simple.

Interestingly enough, Einstein himself stated that the acceleration was the only possible explanation. Which of course it is. It's a lot easier to think about this if you start with the twins on board two different spaceships (rather than one being on the earth, which tends to make people automatically think of it as "immobile" while the spaceship is "moving" - but why?). It is impossible in special relativity to get rid of the symmetry issue the two reference frames, because it only deals with inertial (that is, non-accelerated) frames. Acceleration is what makes the difference. Just like Einstein said.

Ohhh no, I did not understand the point with the 2 frames .. and that was key... :-(

The youtube series of Fermilab is by far the best I've ever seen among popular physics explanations. But I'm still trying to wrap my head around this one. If I understand it at least partially, then the apparent paradox from the original 'twin paradox' (with Ron and Don) stems from the fact that Ron _returns_ to Don and thus to Don's reference frame. Is this correct? Would thus the following be correct: Let's say, instead of Ron _returning_ to Earth, Don _follows_ Ron to Alpha Centauri. That is, once Ron reaches Alpha Centauri, Don starts from Earth and upon reuniting with his twin, they find out that now _Don_ is the younger one. (Though maybe that is problematic to say: what would "once Ron reaches Alpha Centauri" mean in this context from Don's perspective?)

You are a great video personality mr Lincoln. Keep these videos coming please!!!!!!!!!!

You are only talking about Special Relativity. Relative acceleration does play a role in General Relativity, where a single non-inertial reference frame is allowed for the spaceship’s entire journey. The person in the spaceship can believe that he is standing still by believing that there is a gravitational field present throughout all of space, and that gravitational time dilation is what causes him to be older than his twin.

I'm quite disappointed with this "real" explanation. Isn't "frame jumping" just acceleration? I find the difference only semantic. Although it is wrong to say time dilation happens _only_ because of or _only_ during acceleration, I'm not aware of any person with any relevant credentials claiming this.

I've found many different explanations of this paradox, involving acceleration or frame of reference change, but for me it could be solved in a simpler way. I don't know if I missed something, but here's my interpretation of the paradox. Let's assume the twin on the spaceship travels to a nearby star and comes back, then the situation for the two twins is not symmetric. The twin on earth sees the distance segment Earth-star as stationary, so he measures its maximum lenght (l0). The twin on the spaceship instead sees the distance segment as moving, and thus he measures its contracted lenght l. The twin on earth sees the other twin complete his journey in more time since he measures the time of the trip as t=l0/v, while the twin on the spaceship measure the time of his trip as t0=l/v. Since l

Awesome video and explanation. Like always.., Thank you!

Ron needs to fly 8 lightyears and it will take him 4 months. Does he need 8 years worth of fuel on the spaceship or 4 months?

Help from a physicist please: Don says that there is no acceleration in the case of the twin paradox - but isn't the transition from one reference frame to another what acceleration is? Where am I going wrong here?

That was great! Thanks, Also thanks for including the equations. That helped.

So the twin who lives the longest is the one that goes from one inertial frame to another and back. This is also called "acceleration".

I have a notepad full of scribbles which give a very impressive look to my total failure to perform the transformation. I'm not even sure how the additional reference frame solves the paradox. Still, there's nothing better than having something you firmly believed shown to be completely wrong and I'm not beaten yet. Back to my scribbling I go...

"I'll pause for a moment so you can look at them..." LOLOLOLOL!!!

The thought experiment doesn’t clearly factor out acceleration, because it seems ‘B’ and ‘C’ are stopped and only start moving when the experiment begins. If both are ALREADY in constant motion, and ‘B’ passes ‘A’ at time zero, and ‘C’ passes location ‘3’ at time zero, then no one is EVER accelerating. And, FWIW, I was surprised there was no mention of how a traveler - whose clock seems perfectly normal to them - can make the trip in such a short time: Because the distance appears much shorter since the traveler perceives space moving past them.

Awesome video, comfortable information density, cool production. Don't ever apologize for the length if the subject needs it! Looking forward for the next one ;)

sir, suppose both Ron and Don are not familiar with STR & time dilation. Now Ron knows it will take him atleast 4yrs to reach the star since his ship travels at 0.99C. But due to time dilation he realizes he has reached in merely 22 mnts. So he decides to crosscheck his speed and finds out he must be travelling at 2.2C to cover 4 light years in 22 mnts. How is this possible,please explain?

So to solve the Twin Paradox you actually need a triplet?

Can you make a different twin paradox example using A, B, and C experiencing different gravity? Maybe all three are stationary to all observers. Then a black hole moves through the single frame of reference, with A, B, and C at different distances from the black hole. The gravity of the black hole attracts the three observers A, B, and C. Normally this would make the observers closest to the black hole appear to move faster, relative to a fourth observer. But remember in this example all three appear stationary to all observers. So for example, if A is closest to the black hole, A must accelerate away from the black just enough to have no apparent motion relative to itself or any other observers. The same for B and C, although they will require less acceleration to appear stationary because they are farther away from the black hole. After the black hole passes, all observers agree to have observed no motion. However, observer A will have experienced the less time than B and C.

I would have liked you to have spoken about the time gravity relationship, and that position and velocity can be seen as being relative to centres of gravity, such as stars and planets at this level. Any chance of a video on this?

Dr. Don Lincoln... my guy! :D

I gather from this video that acceleration myth has been busted. Youthfulness is proportional solely to the number of reference frames, whatever the method of counting those frames is. Now, why did physics design such an awkward thought experiment 100 years ago, full of unnecessary circumstances? No wonder it lead to the myth. Studying this newest explanation (by the way, it's somewhat hard to grasp when sitting here looking at the explanation from the fourth reference frame, looking at paradox that cancels out with another paradox sort of stuff) I can't help looking for simpler explanation. Perhaps some explanation along the lines on how one gets minimum youthfulness in absolute zero temperature environment and every moving beyond that then increases youthfulness, up to a photon in vacuum that doesn't age at all. Something simpler that is. The slippery relativistics make my head spin.

Genuine explanation! Your guidance saved me a lot of hours thinking :-) One remark, typo?: I think the basic form of the Lorentz transformations should be with "minus".

The 3 reference frame illustration is great. I think there should be a clear statement in the video that there is no paradox - the person 3rd frame reached the starting point and has different age but he started at different place. When twin moving away returns to same ref frame (as opposed to staying in ref frame moving back) , his age would be same as 1st twin. All we have shown is that time passes differently for different ref frame - but that is setup we started with when deciding to use Lorentz transformation. I would prefer a general relativity example which can happen in real world rather than a thought experiment

Acceleration isn‘t the cause! That cannot be stressed enough, as it is such a widespread misconception! So thanks a lot for that superb video on this topic, Dr. Lincoln!

I don't understand. The only reason why we know we need to describe the space ship with two reference frames is because we know it is moving. If we observed this situation from the space ship's point of view and considered the stationary person as moving away and towards the space ship again, we would also need to use 2 reference frames to describe the stationary person from the space ship's point of view. I think my question is "how do we know what is moving and what isn't". Is it because the ship is expending fuel that we know that it is moving? But it isn't, because it isn't accelerating. If the ship stayed at the star, would there still be an age difference? Because at that point, even if we considered the space ship to be moving, we would only need one reference frame to describe its movement relative to the stationary person. I have a lot of questions and I cant find the answers to them. If anyone has any insights, please help. Edit: I think the question I am most baffled about is "Why do we know the movement of the space ship (and definitely not the movement of stationary observer when observed from the space ship) requires two reference frames?"

At 10:23 the video shows that the value of x for the event II in the observer C's perspective is γL, but I got 2γL. (My results for all the other values correspond with your solution.) Is there an error in the video? If not, how did you get γL?

In the video Ron is able to travel to Alpha Centauri, a distance of 4 light years in what appears to him as just 2 months at the huge speed he is travelling. I guess the reason this doesn't violate faster than light travel is because Ron sees the distance between Earth and Alpha Centauri dramatically length contracted so that his speed still remains at 0.999c (the same as that observed by Don). However, what would ever be the need for warp drives/wormholes etc to travel across large distances in space because special relativity essentially does exactly the same thing by "warping space" due to this same length contraction? By making gamma sufficiently large and travelling fast enough couldn’t we reach literally any point up to the Hubble Horizon within a human lifetime (even if humans wouldn't survive that rate of acceleration)? Granted 100s of millions of years could have passed on Earth but my point is that no part of the reachable universe would be off limits for human travel. We could even put all of humanity in a spaceship and genuinely move them to the other side of the reachable universe in perhaps just a few generations. All that would have happened is the universe and our destination would have moved far, far into the future in relation to us? I suppose the only limiting factor is how fast you can accelerate and decelerate (now in the realms of general relativity) the spaceship without proving fatal to the passengers. However, even a spaceship just accelerating constantly at 1g could reach vast, vast, vast distances (perhaps billions of light years) within only a few hundred years. I guess the problem is ever being able to continually accelerate to get close to the speed of light. As speed increases so too does mass and therefore a spaceship would require ever more increasing energy to continue to accelerate at g. In all practical senses getting anything with non-trivial mass up to relativistic speeds would require prohibitively enormous amounts of energy.

From C's reference frame, A and B are approaching, with B approaching at twice the speed of A. Clearly, from C's perspective, B will have the slowest moving clock and A slower than C's but faster than B. From B's perspective both A and C are moving at the same speed, so they have the same gamma factor. I fail to see how seeing things only from A's frame of reference explains the "paradox", because it results precisely from the apparent disagreement of what different frames of reference would predict. What we need to show is how all three perspectives are consistent.

This is very interesting. Could you recommend a text book for new learner like me in order to explore more? Thank you sir.

I am grateful for these clear and sure explanations.

I just dont understand how to find v when i put everything into the Lorentz Transforms, there is something I am missing. Can anybody help?

The change in direction is not acceleration? On a trip to a star do the accelerations at start and end break the symmetry and make the subjective time shorter for the one-way traveler than the LY distance of the trip? Is the return trip required?

Watching 5 years later. Thank you Dr. Lincoln

You should explain why the Lorentz equations were not used for Obs A. And I guess that's because Obs A sees the distance L as static, not in relative motion. As you said, "remember that location 2 is a distance L away from observer A". Obs B and C do see distances between events as contracting. In the Lorentz transform, both x2 and t2 are related to both x1 and t1, so space and time are connected so to speak. I think "length contraction" is an easier way to see why there is no paradox.

This is an excellent video. I am 71 and could follow every step of the way. I checked all the co-ordinates for the there event for the three observers and they were bang on. This sort of thing should be taught at A level physics or maths. Relativity is a fascinating subject. How about a lucid lecture on General Relativity? I note that many still don't get the message that acceleration is not the cause of the paradox. Think of it this way if acceleration were the cause then the duration of the trip would have no bearing on their relative ageing processes.

I think just doing space-time diagrams is still the best visual way to understand why it isn't a paradox. At least, it makes the 'trick' readily apparent for most of these thought experiments. Even more fun, put acceleration back in, but make it the same for both twins. You have one twin staying on Earth who is sitting in a 1g field the whole time (i.e. standing around at sea level on the Earth twiddling his thumbs). You have the other twin in the spaceship which is *always* accelerating at 1g. He accelerates at 1g going away from the Earth until getting close to his destination, then points himself back at the Earth and accelerates at 1g to return (which involves his velocity going away slowly returning to zero relative to the Earth and then increasing again in the reverse direction to get back to the Earth). Then when he gets close enough to the Earth he points himself outward again and accelerates at 1g to slow down relative to the Earth in order to come to a rest on the same pad he was launched from. So, both twins experience exactly the same acceleration for the entire experiment. Lets ignore the Earth going around the sun and the sun going around the galaxy, etc. But one twin experiences something different than the other, because the two space-time paths look completely different regardless of the viewpoint. This is because the twin on the rocket underwent shifts in his frame of reference that were radically asymmetric from what the twin who stayed on Earth experienced. Symmetry was broken the instant the first twin decided to change the direction he was pointing (in fact twice, but the paradox is solved even with just one frame shift). For even more fun, try using general relativity (since in the above example, the frames are not inertial). I haven't done that, I'd go crazy, but I'd really, really REALLY love to see the actual math. -Matt

Hi Dr. Lincoln! I'm the guy who met you at O'Hare yesterday. Thanks for giving me 5 minutes of your time and sorry I had to run, I had a certain space and time to be at.

Your explanations are extremely helpful

@Fermilab THANK YOU DON AND TEAM! I am an undergrad physics student at UCSB and this just helped me for my up coming FINAL!

Thank you for the great video. However I have a question: Isn't it true that 'B' and 'C' still do accelerate in the time they start moving from A and C respectively, and vice versa when they decelerate to stop in the destination?

This would be a relativistic solution to the "paradox" if the principle of relativity (uniform motion is relative) hasn't been violated. Having 3 observers only complicates the situation where different frames of reference are sloppily switched, almost like a magic trick. Dr Lincoln can breezily claim that acceleration isn't the key to the twin (non)paradox, but he does students of relativity a disservice.

Dear Dr. Don Lincoln. It is a real pleasure to watch your precise and well explained presentations but let me to comment on the current one. The calculations here use the Lorentz Transforms which are derived by using a moving "light watch" (a beam of light reflected between 2 mirrors). One can claim that both Don and Ron may be defined according to relativity as either moving or stationary, but it contradicts the basic assumption of the Lorentz Transform. The "relative" movement of Don relatively to Ron does not allow the use of the Lorentz Transform which are based on actual (not relative) movement of a "light watch".

Although I agree with the point raised in the comments (that the conclusion is terse) I was pleased to have Dr Lincoln, with his broad understanding of the subject, provide a signpost to solving the apparent paradox. There is now plenty of work I need to do, to understand the physics of the twin's mission, but I believe I can safely discard the argument that it is the changes in acceleration that create the paradox and focus on the argument that it is the transition from one frame to another that causes it.