Why twin's paradox is NOT about acceleration?
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- Опубликовано: 20 июл 2024
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Chapters:
00:00 What is the twin's paradox?
00:48 Why acceleration doesn't solve twin's paradox
2:24 Twin's paradox without acceleration (Earth's frame)
4:42 The traveling frame
7:13 My new website - floatheadphysics (ad)
8:48 Earth's frame again - with the flag
11:38 Travelling frame again - with the flag
13:30 The resolution!
14:45 Relativity of simultaneity
17:02 Isn't the root cause the acceleration?
18:20 What do they 'see'?
In this video, we'll intuitively resolve the twin's paradox. This version of the twin's paradox involves no acceleration. And no, you don't need equivalence principle, and you don't need general relativity to solve it. Twin's paradox can be completely solved using special theory of relativity and the correct usage of relativity of simultaneity.
Link to the website:
www.floatheadphysics.com
As a 60 year old physicist, I can say that this is the best demonstration of the twin's paradox I have seen, and I saw the first one when I was 15. I also love your enthusiasm. Bravo!
I'm almost 50.
Thing is, back in the day we didn't have those neat animations, which helps a lot to understand
youre 50 years old and you play minecraft?, is that your kid?@@misterlau5246
This seems promising, let's watch! I watched it and the flag is not giving me a better perspective, the 5 or 35 seems arbitrary to me. It is still a paradox in my opinion.
youre a 50 year old that plays minecraft?, or is that your kid@@misterlau5246
But it's completely wrong. It is all about acceleration.
He replaced one twin and not the other with two spaceships. That completely begs the question.
School taught me how to do maths in physics like memorizing it... but mahesh taught me how to visualize it .. every inch of my understanding of physics has a contribution of him
Powerful stuff!!!
@@Mahesh_Shenoyisn't this change in direction the same thing as acceleration?
it's not physical change in acceleration, but a directional change in acceleration.
i think this language of physics is causing a lot of problems.
as in logic, it's called the fallacy of equivocation. when we think the 1 word means the same thing but it actually means different things in the sentences.
ps. your videos are by far the best on the twin paradox. the others don't even mention Relativity of simultaneity or the different perspectives of the ships/twins.
but it is still very hard for me to grasp as someone who didn't do higher maths.
@@Mahesh_Shenoyp.s.i don't know if this is an accurate metaphor.
but i like to think of the blue spaceship as running away from the light of the earth. so it's like a earth light being a tv monitor that is going from 60 frames per second to 30 frames per second. as the space ship is running away from the light of the earth. like doppler effect.
while the red spaceship by moving towards the earth its fast forwarding through time. so all of a sudden the light or frames per second coming from earth doubles from 60 per second to 120 per second. as you race towards them. running into all of them faster. like doppler effect.
so blue space ship is running away from earth, so from its perspective earth is running slow, like a monitor tv screen film running slow at half speed.
and then when it becomes the red ship, its like the earth's light, earth's monitor suddenly speeds up x2.
like how you can change the speeds of the video on RUclips.
not sure if this is a good way of understanding the time jump, time dilation and Relativity of simultaneity. .
but it seems to help. i think.
one direction you see earths frame rate slow down. the other direction you see all of tbose delayed earth frame rate suddenly speed up and bombard you with it.
like doppler effect. you ran away from your wave first ship. then you turned around and ran towards it second ship.
maybe you should change the color of your ships engine lol. 😂😂😂
I'm no expert. but thanks for the video.
are you kidding folks? nobody has spotted the huge contradiction in this video?
@@anatolyr3589 explain?
I just genuinely love how Mahesh “has a dialogue” with Einstein
The problem is, Einstein doesn't have a dialogue with him.
Yes, that guy again.
@@wesjohnson6833Einstein moved faster than the speed of light (which he told impossible cuz he was scared of future) and talked with this guy and traveled at 0 velocity
The twin's paradox has three velocities: the velocity of the Earth, the velocity of the outbound trip, and the velocity of the return trip. That means there are three inertial frames, one for each velocity. And in special relativity, an inertial frame is an observer. There are three observers but only two people, the twins. This is what confuses people.
Try drawing the space-time diagrams for each of the frames.
In the first one, the Earth is not moving and the spaceships are. Time for the outbound trip is slower than Earth time and time for the return trip is also slower. We have: Earth's time > outbound time + return time. This is the part everyone agrees on.
From the point of view of the outbound trip, the Earth is moving away from the ship, so its time is slower. But to return to Earth, the ship has to leave this frame faster than the Earth or it will never catch up to it. Time for the return trip is even slower than Earth's time. We get: slow Earth time > outbound regular time + even slower return trip.
And from the point of view of the return trip, we get a similar result: slow Earth time > even slower outbound time + return regular time.
I think the space-time diagrams make things a lot clearer.
PS: I have made the space-time diagrams. photos.app.goo.gl/duHuAZtMhMTkuDDw7
@silverrahul I don't understand why "laymen" should be scared of "spacetime diagams". Haven't they been taught in school to draw simple x against t graphs to solve problems about speeding cars and trains?
No, you're simply ignoring the problem completely.
The entire point is that the twin on the spaceship should have just as much right to perceive himself as "at rest" as anyone else. To him, the other twin speeds away and returns.
What breaks the symmetry is only absolute acceleration. The rockets on the ship.
@@MrCmon113 how is that ignoring the problem? I feel like his explanation very much makes sense. But I kinda agree, judging by the video, when the twin "changes direction" the Earth twin suddenly "gains age" and it is directly correlated with the required acceleration.
@@absolutehuman951I kinda agree and want to add: Mahesh never said it's completely unrelated to the acceleration needed to jump between frames, he just said acceleration is not the root cause but rather it is relativity of simultaneity. And that it gives you a better understanding if you think of it this way.
@@Grecks75 This video is nonsense. "You will see for yourself... I know you have many questions". People who don't understand space-time diagrams can not understand relativity. Everyone who thinks he learned anything from this video is deluding himself.
Thank you sir for also explaining the photon part and the age disagreement, it answers my question in previous video about "seeing the future" related to andromeda paradox
Excellent explanation. Thanks again Mahesh. There are very few explanations of twins that even mention simultaneity, you have once again cracked the case by starting with intuition. I would love to help you with the animations, let me know if you would like some after effects help to really bring your message home. Keep it up!!
Thanks a lot :)
This is such a fantastic video, well explained! It seems to me that the explanation for the "lost 30 years" is essentially the Andromeda Paradox. It would be interesting to do a video on the Andromeda Paradox too, and then link it back to the twin paradox explanation here.
There is an interesting technicality that a few people are pointing out in the comments, which I think is worth considering: that your example here does in fact include acceleration, but that acceleration itself has a deeper and more subtle meaning than what we are used to. Essentially, the meaning of acceleration *is* a change in reference frames. Therefore, to say that the change of reference frame is the cause, is equivalent to saying that acceleration is the cause. In the example here, none of the twins are accelerating, but the clock information does accelerate--first it was moving away from earth, then it was moving towards earth, and that is still a symmetry breaking and is, by definition, an acceleration. I like the idea that the argument over reference-frame-change vs acceleration is meaningless, because they are two ways of expressing the same thing.
Yes, nature doesn't care what we call it. Yet there is one difference: We can always accelerate -- it is local and it is a choice --- but without the consistency of light the other aspects fad away.
Great point about the "information" undergoing acceleration. Information may be the only real thing out there.
Well said! What causes the 'paradox' to be paradox-y is that the theory of relativity seems to point to absolute acceleration. Which is confusing since space, time and velocity are all relative in relativity.
I think this bothered Einstein at the time, because he was reading philosophers like Mach who said that all physical quantities (like acceleration) should be defined relationally, not absolutely. I think one of the goals of general relativity was to try to make acceleration relative.
@@marky1312 the "changing rate/direction of change" (acceleration) is relative to "change" (velocity), isn't it?
I used to tell people you can’t resolve the twin paradox because it is the andromeda paradox, once you get the trivial parts out of the way…and they would give me 💩, but minesh is on the 💰 here.
This is by far the best explanation for the twin paradox I’ve seen, and I have watched a lot of RUclips videos on this spanning close to a decade. This holds true for basically all of your videos. Thank you!!
Wow, thank you!
And in 10 years you still haven't figured out that the SR theory is nonsense? The paradox has not been solved at all.
Over 10 years, I've seen plenty of comments like this, too. Yawn.
Superb - I am a professor of geometry, and I never saw such a good explanation without drawing a space-time diagram.
@@kuji3009 You have no idea. all you know is what you have been fed over you lifetime, and this is BS. You are asleep.
You are just King of Physics... saw a lot sci channels none of them really explain in such clear way... you are a truly awesome educator!
You did it. You don't leave room for any "but what if" and now my brain rest at last. The explanations with spacetime graphs never left me 100 percent satisfied, because for me there was still "symmetry" but with your explanation there is clearly and visually no symmetry.
What if instead of staying on earth, the other twin travels at the same speed and distance with the first twin, but to the opposite direction?
What about perpendicular direction?
@@hamdaniyusuf_dani In that case both twins age the same number of years. There is no paradox
@@PADARM Have you done the same analysis as in the video, or just quick conclusion based on symmetry?
What breaks the symmetry is absolute acceleration.
@@MrCmon113 do you mean that the analysis in the video is incorrect?
Can’t wait to hear you illustrating GENERAL RELATIVITY intuitively. Must be an even more mind-blowing journey！
If I understand correctly, on the returning spaceship they would calculate earth's clock to be running slow but if they looked out the window they would see it running fast! Earth's clock measures 5 years (from 35 to 40) while ship clock measures 10 (from 10 to 20). However, since the image they see at the red planet is from time 2.7 they will see the remaining 37.3 years of Earth's history sped up (and blue shifted) during their 10 year return trip.
Yes!
But they know it’s Doppler shifted. When JWST looks at a spectral line in a receding galaxy, we don’t say time is running extra slow there and the atom’s orbitals are running slow…we take part of the Doppler out… but not all of it. Now I confused myself. It is running slow…and helium atoms are flat, not spherical like they are here. It’s all relative
17:22 "Acceleration causes change of frame. Change of frame causes relativity of simultaneity. Relativity of simultaneity causes the resolution to the paradox." Based on definition of root cause, this would actually mean the acceleration is the root cause, not relativity of simultaneity. You are correct in saying that relativity of simultaneity is the correct explanation and not general relativity because the thought experience is done in flat space time.
To again ignore the role of acceleration in breaking the symmetry is still an incomplete solution. The explanation in the video shows it is the spaceship that is changing frames. This modification of the original paradox has already assumed it is the spaceship that is acceleraing. But if you do not consider acceleration and the fact that it's absolute, the people on spaceship can say it is in fact the people on Earth who are changing frames. Then you can construct an symmetrical situation with this scenario (i.e. the original eEarth is always moving to the left, then a second earth moves to the right during the change in reference frame, there is only 1 spaceship that is stationary and remains in the same frame, and the ropes are attached to the earths instead of the spaceships) and the math all works out to be the same and the paradox would still be there.
Ultimately, you can explain the discrepancy between the twins' age due to their relative movement in variety of ways, such as through relativity of simultaneity, change in frames, doppler, space time diagrams etc, but all these explanation are incomplete without incorporating acceleration to break the symmetry, i.e. it is the spaceship that is accelerating and not the Earth.
@silverrahul Yes, and it's as if you didn't bother reading my comment before replying
It depends on how you define root cause. To me (and to Mohesh) the definition that is the most useful is that the root cause is the deepest cause that is present in any scenario, and is still explanatory. Acceleration is only present in some versions of the paradox and not others, therefore it can't be the root cause by this definition.
It's like if you're trying to explain why people get colds. The root cause of getting a cold is that someone is exposed to and infected by a virus. Getting exposed and infected has its own causes of course. Maybe *you* got a cold by going to the movies, and for your individual case it is valid to define root cause this way; but saying that that root cause of getting a cold *in general* is going to the movies makes no sense at all. So if you are trying to understand colds in general, it makes sense to say that the root cause is exposure and infection by virus, because those are true in every case. Of course, it is still helpful to understand how exposure and infection happen, because understanding the causes of those things is still helpful in preventing colds. Similarly, the root cause of the twin paradox is changing reference frames. But it's still helpful to understand the cause of that cause, which in many (but not all!) cases is acceleration.
@@erinm9445 "Acceleration is only present in some versions of the paradox and not others, therefore it can't be the root cause by this definition."
The problem is in this statement. Acceleration is in fact stil in the paradox, albeit hidden. The change from the original version with the 2 twins to this modified version with has already used the absoluteness of acceleration to break the symmetry in the first place. Let me explain why this is:
In the original version, the earth person (A) sees the spaceship person (B) leaving and then returning. There is a change in reference frame for B, so in this modified version, a third person (C) is introduced to eliminate the acceleration of B, but instead the two different frames are represented by B and C. I will call this scenario 1.
However, in the original version, B also sees A (and the earth) leaving and return. From his point of view, he is stationary, and A is the one who is apparently accelerating. If B were to modify the thought experiment into this modified version without acceleration, he would be completely stationary throughout the entire thought experiment, A and earth travel constantly to the left, and a third person (C) would be travel towards the right, passing A and syncing clocks with A when he passes A, and then meet up with B to compare clocks at the end. In this modified setup, B is in a single reference frame and A and C are representing the two different frames. All the math is the same as in the video and B would conclude that C's time would be younger. I will call this scenario 2.
If we were to ignore acceleration or to say the paradox does not have any acceleration, there is no basis to choose scenario 1 over scenario 2 and vice versa for the modified version. The only reason that scenario 1 correctly represents the original paradox and not scenario 2 is because in the original paradox, A is truly not accelerating and B truly is accelerating. In other words, when this video is selecting scenario 1 instead of scenario 2 to illustrate the solution, it has already used the fact that acceleration is absolute when doing so. The rest of the analysis no longer requires acceleration, but the initial set up of this modified paradox did require it.
@@ToboGamers I honestly couldn't follow everything you were saying here (not a criticism, I can't really parse dense physics arguments in paragraph form). But if what you're trying to say is "changing reference frame *is* acceleration, by definition, so Mahesh's example here actually does have acceleration, just not the kind we're used to thinking about. There aren't any twins acceleration, but the time information *is* accelerated when it moves from one ship to another", then yes, I think that is probably right.
But that is not the definition of acceleration that most people use, even someone with an undergraduate physics degree would not use that definition. So if you want to claim that the clock information is in fact accelerated, then that is a pretty technical definition that needs to be called out, and recognized as a very specialized definition of acceleration.
@@erinm9445 That's not actually what I'm saying, but I'll say what I said in my previous comment a bit simpler.
As demonstrated in this video and as you have stated, by using two different persons to substitute for the accelerating twin in the original version, acceleration was removed in the modified version. But deciding on which twin to replace with the two different persons depends on which twin is accelerating in the original version. Twin A would want to replace twin B with two persons, but twin B would also want to replace twin A with two persons.
The correct analysis is to replace with accelerating twin, as this video did. The only justification for this that he was the one who is truly accelerating. Therefore, acceleration is still required in the complete answer. The video simply ignores this part when he replaces the original paradox with the modified one.
Very well done. Such great videos!
Bro this guy is succeeding fenyman in his teaching skills at this point 😅
Great video. Simultaneity in relativity is often overlooked. Nice explanation of why you can't ignore it. And it was great to highlight that what you measure using scientific apparatus, clocks, rulers etc is not the same thing as what you a see using your eyes or cameras. Nice.
I do hope the author of the video reads this. Who y'gonna believe, science or your lying eyes.
Absolutely..Too many explainers just handwave away the idea that an 'oberver will see ..' without bothering to consider such things as light takes time for seeing to occur.
Best teacher I've ever seen! ❤
That was such a good experience. I'm simultaneously Happy, impressed, dazzled, and awakened. I understand others comparing this to other explanations, but I want to say this is the first time it's ever really been explained. Your approach of having a conversation and asking all those questions is so incredibly effective. Thank you so much. Special relativity is itself an amazing leap of imagination. And then on top of that solving the paradoxes are a bunch of other giant leaps.
I liked your explanations in the first 18 minutes of the video, but I felt like you were missing a key part of the explanation that would make it more intuitive. But then I saw the final section starting at 18:20, and I was very happy to see that you covered the key part. Your explanation was great!
Another way to think about it is if you don’t have a frame of reference switch and stay in one frame of reference the whole time. When the twin flies away from earth the twin is at rest. if we stay in this frame of reference when the twin turns around, the twin agrees that she is moving left with respect to her initial frame. And she will say that she is moving left at twice the speed than what she would be moving left at from earth’s perspective. So I suspect that the increased time dilation and length contraction she accounts for then what earth accounts for will make up for the time dilation and length contraction she didn’t have from her frame of reference in the first leg of the trip.
That is how I thought you should explain in the first video.(the rope one)
But because of my SSC exams I don't want to use my brain in understanding this video. But this video looks great. The hardest part in understanding physics is using imagination. This video makes us to them imagine easier.
SSC-2024 here🫡
Notice that what you call ‘jumps in time’ only occurs when there is acceleration. Acceleration can then be called ‘traveling’ into the future frame of a locus of regions where the magnitude of the ‘jump’ depends on distance to regions.
I thought of this with your last video on the triplet paradox, and realized that changing reference frames is the only reason the turnaround matters. If we turn the accelerating frame into 2 non-accelerating ships, then that twin’s “acceleration” just moves her into the first non-accelerating ship’s reference frame, and the turnaround “acceleration” moves her into the other ship’s reference frame. In your last video, the radio tower between the planets helped me see why those reference frames have the opposite planet clock 7.5 years ahead of the close-planet clock. Those reference frames exist regardless of any acceleration, as discussed in this video you can move a clock into that reference frame by beaming a signal, but acceleration is just a different way for someone to move their clock into each of those reference frames. I finally intuitively understand the twin paradox after years and dozens of videos, thank you!!
Your RUclips pacing is absolutely perfect. Again, another epic video.
Fantastic video with a really wonderful examination of this puzzling paradox.
Excellent... the final bit really helped!
Thats insane! I wasn't expect to take anything more from twin paradox, but that is so cool. The best video i saw for last 2 month.
I think relative simultaneity is the only reason for everything, including length contraction. Like in order to measure length you need to connect space separated points, f.e. with ruler. And that takes time to move its end to correct place.
All three effects - time dilation, length contraction, and simultaneity - can be derived from each other, all of which is a consequence of constant speed of light. I find this so wholesome (and satisfying).
Yes, but it’s not that it takes time to move, it’s that if you’re in the middle of the ruler, your definition of now at the front end is in the rulers past, so it’s closer to you. Back of the ruler is in the rulers future, so it’s closer to you: boom, ruler shorted.
Note that this works with atoms, without Lorentz transformations. If you solve the ground state shroedinger equation of a moving proton, with its electric and now magnetic fields and a moving electron, the answer will not be a spherical orbital…it will be squished. Length contraction is real at the at of level.
Actually, it’s really at the quark level too, but that’s a longer story.
That was the best non-math explanation I have ever seen. How about a take on the "gravity is not a force" thing as well.
Brilliant! Thank you so much for your work!
Why focus on denying acceleration when the solution is acceleration × distance / c²?
Hi Mahesh! Excellent work and real mind-bender of a concept. If I may offer a suggestion, I think the point would have really been hammered if you showed the length contracted version of spaceship 1 from the frame of spaceship 2. The reason is that there is a third spatio-temporal simultanety event that appears to be violated (i.e. the simultaneity of the ends of the two ropes being at earth at the same time (at time 20). A visualization of this simultaenity in the three frames of reference would have made a lot of sense.
I watched lectures of another physics professor on the SR topic in the past (he did not have such high-quality visualzations, though), and back then I already got the impression that profoundly or intuitively understanding relativity of simultaneity is key to understanding all of SR. There isn't as much talk about it than about time dilation although it is such an important aspect or result. I would love to see another video on relativity of simultaneity with another example.
the IDEA that whether two events that are separated in space happen at the same time is not absolute, but depends on the observer's reference frame.
That's the crux of the problem. You are conflating information with time. It doesn't work that way.
Causality. Cause and effect.
The traveling twins ship blows up. It takes 6 months for the EFFECT to reach Earth. Is the twin alive or dead? You won't know until the wavefront collapses. Aka, stops transmitting.
You don't see things in real time. You are always experiencing the past. Lightning strikes a tree. You don't know that until the effect arrives at your location in space.
What I don't understand is why you don't understand that light is no different than sound. They are both just carrier waves. Other than c being absolute acceleration, they are essentially the same because the laws of physics are equally applicable in ALL frames of reference. Including the frames of light and sound.
E=mc. Everything is an emergent property of acceleration.
F=ma. Force equals Acceleration and Acceleration equals Force.
Acceleration in space equals Acceleration in Time.
The inverse square law of motion. Force decreases with distance.
Information about an event (when it takes place) is moved further back in time.
Betelgeuse. 500 light years away.
When it explodes you will think it's taking place in real time. That's the IDEA of simultanaeity. That doesn't mean they are OCCURING at the same time.
That acceleration free thought experiment is not the twin's paradox. It's simply what you get with three inertial frames of reference with their own clocks. In the case of the true twin's paradox, there are just two clocks, one with each twin. If you can work out a way in which the twin and his/her clock can jump into the frame of reference of the right bound rocket without undergoing acceleration then, on reaching the red planet, jump into to the frame of reference of the left bound rocket without also undergoing acceleration then you have the twin's paradox. As it's shown, you have just presented a different scenario altogether which is not the same problem. Nobody thinks it is.
The only thing that breaks the actual symmetry of the twin's paradox are those two changes of inertial reference frame of the "travelling twin". If you know of a way of a massive body changing inertial frames of reference without undergoing acceleration, then I would be interested to hear it. So if you want to simply explain the twin's paradox as simply there two changes in inertial reference frame, then fine, but do not claim there is no acceleration involved. There is with the problem as originally posed, but the thought experiment shown is not that problem, nor was it ever a paradox.
As far as I can see, there is no way of the travelling twin and his/her clock doing those jumps in inertial frames of reference without undergoing acceleration.
For me it gets more intuitive and clear when looking at a spacetime chart and drawing planes of simultaneity for different observers, seeing how they rotate by Lorentz transformation. We all live in the same 4D spacetime, we just slice it differently with our different coordinate systems.
Yes, this is the most intuitive to me as well. But it does leave me wondering how meaningful the idea of that coordinate system slicing is, outside of the math. It is an invaluable accounting tool, but to me it says that the idea of "now" is a fiction, unless you're talking about things that are happening locally; the meaningful thing is only what can reach you. So in the video, receiving the photo from a 2.7 years older earth is meaninful.
@@erinm9445 Well, we all can only observe something right here, right now, locally. Lorentz transformation keeps light cones intact, those form certain causal structure, but all the distant things we can call "now" are outside our light cones and can never be observed directly, so there's a lot of leeway in choosing what to consider "now", we're somewhat free to mentally project what we think "now" is at distant points... The "now" plane doesn't seem to be so rigidly defined as causally connected events. (just thoughts without a very clear conclusion)
@@thedeemon For me, the explanation in the video is more intuitive than the spacetime chart because with the spacetime chart I always have the question: Wait, wouldn't the graph be the same as the one of the ship, if the earth is the one that leaves and comes back? but with this video I have no room for doubt and my brain is at peace now.
@@PADARM The question at the end is valid point! But the reason you cannot do the spacetime diagram in which the earth goes away and comes back is that you are not allowed to treat the spaceship as an inertial reference frame for the whole trip. Because it accelerates at the turning point. In this videos scenario you cannot think about putting the "travelling twin" only in one reference frame because there are two ships that are clearly in different reference frames.
I am so glad I found your channel.
Welcome!
Love seeing a teacher passionate about the subject they're teacher. Keep it up!
Stra giga like, as usual! You're great, keep going man
Relativity is the very engaging topic possible only when mahesh sir turns around.Keep doing your good work sir.
First view sir. Thank you 🎉for your videos expecting this long time.
Oh yea! More to come. More to come!
Sir, what about quantum? And electromagnetism? I also want vids on it!!! @@Mahesh_Shenoy
Also would u explain everything from basics in quantum mechanics like u made the series of relativity , including works of shrodinger, broglie, and maths behind quantum? Ik it will take a long time.. and m ready to wait.. but I would like to see ur response on this!
this is gonna be so good
Relativity of simultaneity is the key consideration "overlooked" in most, of not all, special relativity paradoxes.
I KNOWWWW!!!!!!!!!!
Relativity of simultaneity is not important to this at all. The question isn't "how can people experience different time". The question is: "What breaks the symmetry?"
Just an unbelievably great explanation!
But he is still wrong. There is no solution for a paradox. The theory is nonsense.
I watched the video to stop thinking about this, but the end Mahesh says, this will keep you thinking for a long time.
Hi, Mahesh. Will you make videos about general relativity too? I really hope so. General relativity is something I never understood, but I am very confident you could make us understand. Congratulations for these amazing videos..
Congratulations on the excellent presentation. The described "third spaceship" solution is a good way to understand what actually happens with perception of different clocks during the acceleration of the spaceship twin. It is good to understand this solution to get a better intuitive understanding of relativity of simultaneity.
But it does NOT solve the paradox without acceleration as you claim it does.
For your explanation, you have chosen a scenario that uses another spaceship traveling in the opposite direction, and the spaceship twin jumping onto that spaceship.
That choice of scenario is an arbitrary choice. There is no a-priori reason to make the spaceship twin jump ships, instead of the Earth twin.
You could just as well choose a scenario where the earth twin makes the jump instead, and the spaceship twin never does. Suppose, from the spaceship's perspective, the following happens:
The Earth is initially moving away from the spaceship. At the turning point, the Earth meats up with a second planet that is traveling in the opposite direction (towards the spaceship). At the moment Earth reaches that other planet, the Earth twin jumps onto that other planet, and they travel towards the original spaceship. When the second planet reaches the original spaceship, they compare clocks.
Nobody accelerated in this alternative scenario either, yet in this alternative scenario, less time passes for the Earth twin, than for the spaceship twin. That is the opposite from your scenario. Hence the paradox is not resolved.
So which of these two scenario's must be used to solve the paradox? Does the spaceship twin jump onto another spaceship, or the Earth twin jump onto another planet?
It is the ACCELERATION that decides which scenario is valid. The twin who accelerates is the one who changes reference frames, and therefore the one who jumps onto another ship/planet.
It is only the acceleration that solves the paradox.
@silverrahul _"this is the same premise as the one in video"_ - exactly., it is the symmetrically opposite scenario from the one described in the video, with a symmetrically opposite result. Therefore, they cannot both be correct. Hence there is still a paradox.
_"there is no acceleration involved."_ - there is acceleration involved in choosing the scenario. The acceleration determines which twin needs to jump ships/planets, and therefore which scenario to choose for the explanation.
@silverrahul _"In your example, you switched the names, so earth twin is younger."_ - I did not switch names, I chose a different scenario. In my scenario, the Earth twin ages less. In the scenario chosen by the video, the Earth twin ages more.
Without referring to acceleration, there is no reason to choose one scenario over the other. Therefore, there is still a contradiction.
It is very easy to understand when you don't start one twin on Earth, and the other in a spaceship, but place both of them in identical spaceships instead. One is in spaceship A and the other in spaceship B. A sees B move away and then return. B sees A move away and return. For which of the twins does the "third spaceship" need to be used in that case?
_"there is no jumping ships/planets"_ - the "jumping" is just a metaphor for changing reference frames.
@@renedekker9806 "the "jumping" is just a metaphor for changing reference frames." In order for your argument to be valid, you have to explain why syncing clocks is equivalent to acceleration. There is no jumping, and using that word (which does inherently imply acceleration) is a dodge.
The only argument I can see for why synching clocks implies acceleration is that for information to be sent and received, physcial processes must happen in the ships' computers, and those physical processes require acceleration of mechanical parts. But that seems very weak. That is just acceleration happening within the ship, not too the ship. The earth and ship are both experiencing all kins of internal accelerations for the entire journey, but those are meaningless to the larger problem.
@@erinm9445 _"you have to explain why syncing clocks is equivalent to acceleration. "_ - it's not. Changing reference frames is equivalent to acceleration. That's what acceleration does, it brings you from one inertial reference frame into another. You might want to watch the video again.
_"...but those are meaningless to the larger problem."_ - you are missing the point.
It is very easy to understand when you don't start one twin on Earth, and the other in a spaceship, but place both of them in identical spaceships instead. One is in spaceship A and the other in spaceship B. A sees B move away and then return. B sees A move away and return. For which of the twins does the "third spaceship" scenario need to be used in that case? And based on what do you decide that?
@@renedekker9806 I run accross your comments frequently in the physics videos I watch. You are clearly really smart and knowledgeable on the subject, but there is so much unnecessary condescention in your argumentation. You often make unexplained assumptions in your writing, and then get frustrated/belittling when the person you are responding to doesn't share the same set of assumptions. Maybe those assumptions are warranted for someone who has a PhD in physics, but they are not warrented in youtube comments, where 99.9% of people do not have a PhD or even an undergrad degree in physics. I think that you'll make much more headway in your attempts to educate if you keep your audience in mind, and recognize that while your knowledge is rarely at fault, your explanatory clarity (to someone who is not an in-the-trenches expert anyway) is not.
Mahesh, If you dig into it even more, you will reach the conclusion that the only reason for length contraction is ACCELERATION!
best teacher in the whole world ! 2024's Richard Feynman... Who agree like here !
So much explanations of twin paradox out there, but your's is the only one that gives a good explanation without that weird feeling that some things don't really make sense.
Your prefious video on twin paradox I find completely right as well except that there was an example with deceleration and acceleration, while here is the same without it but with opposite directions of motion.
It is still hard grasp as time here not as intuitive as we experience it differently, but still even in this example it seems that the only difference between the rocket and earth that breaks the symmetry is changing the direction of motion which could be done by either acceleration or by introduction of the second rocket.
Eventually some explanations that refer to coordinate transformation and change in direction due to acceleration make much more sense now considering propper understanding principles of lenth contraction and simultaneousity.
Relativity is so mind-breaking - it's fascinating. The only thing I have serious issues with now, is how comes the time dilation and length contraction calculation come from geometry of vertical clock? If we consider the information speed as C then shouldn't the passage of time depend not on vertical photon clock, but on photon moving in a circle to make more sence?
Oh my god I'm going to have to watch these videos so many times until I fully get it, I can already tell.
But this is the only video that actually resolves the paradox, which is amazing. I have been pestering GPT4 about this paradox, and it kept saying "acceleration, acceleration, acceleration" and it kept failing at the point of relativity of simultaneity. Maybe GPT5 will get it! Lol
Please don't rely on GPT to answer your relativity questions :D
@@Mahesh_Shenoy As of January 2024, that is definitely the truth! 😅 Hey, love your Socratic dialogue teaching style and enthusiasm! Keep making the best vids!!
By far the best explanation of the twin paradox.
However if acceleration has NOTHING to do about it, then you can attach a rope to earth instead of the spaceship, end get the exact opposite result, just using 2 earths. Hence even if the paradox is not general relativity related, still the accelerating time frame is the one that will stay young.
Yaayyyyy congrats on 100k subs 🥳🎉 right as you estimated, around 11pm.
Thank you!!!!
Nifty. For anyone interested, it's pretty old now but Brian Green's free special relativity course on world science u website was really some next level stuff, especially at the time. It's quite comprehensive regardless & there are interactive demos with every chapter. Not sure where the actual demos stand now BC they had to update them for browser compatibility a few times. Also there was a long comprehensive version & a short(mathless) version called spacetime & Einstein.
Very good, lengthening the spaceships with the rods is a very good way to show how the asymmetries created by the length contraction affects spacetime. No other video on this topic that I have seen on RUclips has gone into this in such detail... if at all. The age difference between the twins is less due to time dilation, but simply due to the fact that the traveling twin arrives at the destination at a different time than the twin on Earth observes. As you move quickly in one direction, events in the direction of movement move closer to you from the future, while events in the opposite direction of movement move away from you into the future.
Yes, I enjoyed animating it as well :)
I don't think the events move in the future or past, it is just a delay in observation. They stay pretty much within the same time interval.
@@trevoro.9731 Things in the direction of movement really do happen earlier, which is why the traveling twin ages less: he arrives at his destination earlier. This event occurs later for the twin on Earth because he has a different perspective on space-time. Events are therefore not moved within space-time, but by speed or acceleration you get a different perspective. Imagine you have a magazine with a picture of a person on it. If you turn the magazine slightly so that you are looking at it from the side, the photo will become smaller for you... although it is still exactly the same size as before. This can be compared to length contraction. One side of the magazine will simultaneously turn towards you and the other away from you, making one side appear larger than the other in perspective. This can be compared to the relativity of simultaneity.
@@TingleCowboy I understand it as slow down of energy interaction for one twin, the time doesn't really slow down and remains the same. The perception of the time is different, and that it it. I don't get why adopt such a complex way of thinking. The perceived time or the time when you get information about the event doesn't matter. For me there is no paradox once you accept that the time is absolute, but the speed of energy interaction and therefore perceived time may differ. Even if one twin aged by 2 days, while the other aged by 20 years, the time relatively to the other one is still 20 years, just the perceived time in the exact spot is different. The c "constant" is different locally for both of the twins, and that is it.
@@TingleCowboy Also, I understand the aging of the traveling twin as a result of gaining energy relatively to his inert mass, the more energy he has, the greater the energy interaction is slowed for him at his moving point. But the time remains the same no matter how fast he travels.
On the "dialect" channel one of the videos has a pointer to a paper where They Did The Math. It turns out if you have gravity, you can make the person who accelerates older or younger, and have neither accelerate and be older or younger. You can have one space ship orbiting (inertial movemet) in space while the other holds itself still in a gravity field (accelerating), or you can use a "gravity slingshot" to turn around without accelerating. The only way to figure it out is calculate the path thru four-space / spacetime and see which is a longer time difference.
But this gives a great insight into relativity of simultaneity.
The people in the spacecrafts-if they understand relativity-really shouldn't be fighting each other over the elapsed time on Earth. Each would know that the other sees a different picture of events, and that both are correct in their respective frames of reference. For example, the chaps flying away from Earth would say, "According to us, Earth has aged 5 years, but according to you, Earth should have aged 35 years." And-provided nobody made a mistake in calculations-the chaps in the other spacecraft would say, "That's right."
Suppose you and I stood facing each other a couple of meters apart, and a dog stood between us. I would say "The dog is facing towards my right, which is your left."
Of course, when I was very young, I didn't know that different people could have different perspectives. At that age, I believe I would have insisted that the dog is facing towards *the* right (not "my" right), and I would've fought you if you contradicted me. Then again, nobody let me fly spacecrafts at that age!
well done.
I think the final climax helps a lot !
0:56 „Acceleration is absolute“ Question: In which regard is acceleration absolute? In terms of the presence of acceleration (yes or no)? Or in terms of its value (all observers agree on its value)?
You can feel acceleration. There is no ambiguity about who it is happening to. You might see earth accelerate away in the window, but you'll agree that it is you who is feeling the acceleration.
@@akaHarvesteR The reason for this is that acceleration requires a force, right? But apart from human senses, how can we know which object is accelerating? Change in frames of reference leads to emergence of forces which can be applied here too.
I had the same sensation when I was challenged with this kind of paradox, but in my case, the traveling twin was describing a huge circle that touches the earth at one point.
They argued that the acceleration could be made as little as desired.
It was nice to see, how the earth twin aged like crazy, when the other twin was in the ppposite side of the circle
as always, MAHESH SIR ROCKS
If you think about it, the view from the spaceship and the view from the planets were not symmetric to begin with. From the planets' view, only the spaceship gets contracted, and no other path or distance is contracted. But from the spaceship's view not only the planets, but the distance between them gets contracted. In a sense, only the spaceship is moving and everything else keeps the distance between themselves fixed relative to each other - so they are "stationary". For example, if you choose two points inside the moving spaceship and a drone flies from one point to another, the drone is moving inside the spaceship, not the two points as the points are maintaining their distance fixed between them.
What will happen if we send two twins in opposite directions in two spaceships traveling at the same speed? And they then turn back and meet at the same point again? The situation will be symmetric from the both twin's point of view in that case.
Did you do a video on how an Einstein Cross can predict when the next part of the cross appears?
It would be neat to see how each ship sees the other ship's rope.
Mahesh, you are the best, I watch all your videos. You are awesome!
Outstanding Sir 🎉
Hey sir! Great video!
I kinda have an opinion. This might be wrong but please have a look.
When we are looking things from the perspective of the space ship ➡️, the space ship ⬅️ is moving left of the first one with even greater speed than the earth. So if we consider the perspective of one space ship ALONG with the movement of another space ship (length contraction, time dilation and all)in animating, maybe the "time jump" type of thing might become a lil more intuitive.
:)
The intuitive explanation is that the "turn around" happens in the past relative to the Earth clock. Remember: every location in space is located in the past of every other location in space. The current "now" from any location is an expanding sphere propagating at light speed (usualy this is literally real light).
The outbound spaceship is chasing the "zero" clock time that is traveling at the speed of light. It will arrive at the turn around location 2.7 years after the 0.0 light has already passed that location. The inbound spaceship started years before the outbound spaceship passed the Earth at time zero. The inbound spaceship is "swimming upstream" through the light speed "clock ticks" coming from Earth. (So the Earth is going to be blue-shifted and "sped up".)
Yaa you are correct. I got that . But what I am saying is, in the animation, while animating the perspective of first space ship we only see earth and the other planet. But what does that other spaceship look like from the first ship's perspective?
🎉🎉 Mind blowing bro . After understanding your concept I am going to remain mad for a long long long long long long time 😅😅
Excellent explanation Mahesh.
Congrats Mahesh sir, ur gonna hit 100k soon 🥳 and 1million views for time dilation video
Another way of looking at it is to include the first spaceship in the second spaceship's frame. Ship 1's clock and rope will be distorted even more from Ship 2's point of view, since it is moving the opposite direction.
At 17:22 to me this still sounds like acceleration is the cause, but maybe its just semantics
Like your video, very down to earth explanation!
I am reading a book called Why Does E=MC2? And Maheesh’s videos seem to be ripped straight from the pages. I really enjoy the videos and the book
I have became a fan of you sir
I like the way you explain the things❤
Now I understand! Ty
This is the best explanation I've ever heard for this paradox! Thank you! Also, does that mean the future is just as real as the past? Does that mean the future already exists since there's always a frame of reference where your future is the present? or the past? That's weird.
@silverrahul Right, that makes sense. But even with causality preserved - it still gives me a weird feeling to think that my future is already "written" so to speak. In other words, philosophically speaking here, does this mean an absence of free will?
@chrispyfrenchfries Things are happening somewhere else, and it takes time for you to find out about it.
Every location in space is located in the past of every other location in space.
Your feet are six nanoseconds in the past from your head, and your head is six nanoseconds in the past from your feet.
Alpha Centauri is four years in the past from the Earth, and the Earth is four years in the past from Alpha Centauri.
Any events happening within any three years time period on either the Earth or Alpha Centauri can be arranged so that the events at either location could occur first, or even simultaneously. All possible ordering of those events are valid. For four year periods or longer, then there will be only one possible valid order of events from cause and effect. (But for shorter periods, there is no cause and effect relationship to define a single order of events.)
Our light cones are not changed by a change of frame, Lorentz transformation, so what's in our past light cone remains in our past, what's in our future light cone remains our future, the only events that can "switch from future to past relatively to us" are ones outside our light cones, they are not directly observable anyway, so all this spacetime region outside our light cones is somewhat undefined about being future or present or past for us, the plane of simultaneity that we mentally draw remains just that, an idea.
@silverrahul Perhaps free will was a poor choice of words. I guess what I mean is best given by an example. My death has already occurred in someone's present, their "right now". I'm moving towards that event, but that event already exists out there, it just takes time for me to get to it. Do you believe in such a scenario?
That means how I died, why I died, all the things surrounding that event have already been determined and have been determined for all time? In other words, time isn't something that manifests itself in the present, all of time already exists, we're just moving through it....I don't know it's hard to explain I guess.
Now we are talking about. No acceleration. In my thought experiment I used light traveling back to check time of Earth twin.
This finally makes sense to me. Thanks!
recently found your channel. Peak level explanation.
There’s still acceleration- you can’t ‘remove’ it by considering a different second clock. The second clock becomes the twin, and is accelerated.
Excellent channel … thank you … I can now “kind of” derive e=mc2 from first principles and I understand why photons are massless … not having the same “omg” moment with this one though
Very good explanation. If you draw the timespace diagrams for the earth and for both spaceships and suppose that earth and both spaceships send regularly spaced signals, you notice that everything sets into place but if you attempts to merge the spacetime diagrams for both ships, the trajectory of the earth becomes discontinuous. Because relativity applies only to objects with constant speed…
Luv ur stuff
Very good video! The animations are vivid and very explanatory. The title is a bit misleading, though.... in reality, nothing CAN change frame of reference without being accelerated. It illustrates the steady state approximation after the acceleration part happened... and is correct, but much of the paradox's "meat" resides JUST in that phase. Even in the limit of an instantaneous frame change, with only ONE moment of infinite acceleration (= an _infinite_ force for an observer with mass, because the necessary impulse [DeltaF*Deltat ] is definite) the whole picture changes abruptly JUST there!
(BTW: massless objects cannot be observers: they lack internal structure so they don't have memory, and that is equivalent to say they don't experience time, or space)
Got tears in my eyes at 12:45
☺️
It's pretty simple. Move at a speed comparable to light (a thing that determines the rate of change based on how long it takes to get from atom to atom of the moving thing) and your rate of change will decrease. When the ship moves and the Earth stays as normal, the ship ages slower. When the Earth moves and the ship stays where the Earth was, the Earth ages slower. Forget about perspective during the trip and make measurements at launch and landing. It is then obvious that at halfway, the age of the moving thing will have increased by half of the relatively stationary thing's age amount, as long as the moving thing stayed at the same speed.
I think this is a better explanation than the other twin paradox videos id like to hear sabina's and Dialects response to your video - what do they think?
Can this be applied to quantum particles for entanglement problems?
This is one of the implications of relativity that really blows people's minds, that there's no such thing as a cosmological 'now' but only local 'now' and even different parts of the planet can have slightly different ideas about it given we're moving in different directions as the planet rotates.
Thanks for the video! I understand why time dilation occurs in terms of signals of causation taking longer. Ie, the electrons send a signal to the other electrons, but they are moving fast, so those signals take longer. I find that explanation very helpful. But is there a corresponding reason for why lengths get contracted?
Time dilation + Relativity of simultaneity = Length Contraction!
I feel bad for watching this now in case you think I'm only watching because you changed the thumbnail. I love your video. Thanks for explaining things simply.
This is some great video. Yet, I have a simple question. Starting from 17:21 You say, "Acceleration causes change of frame, causes relativity of simultaneity and relativity of simultaneity causes the resolution to the Paradox so the root cause is relativity of simultaneity"
Let's analyze it shall we?
So Acceleration causes change of frame, Which means that the acceleration is the cause to the relativity of simultaneity. Then you say, simultaneity and relativity of simultaneity causes the resolution to the Paradox, whic means the cause to the resolution of the paradox was the relativity of simultaneity right?
So, if we draw the cause and effect sequence we would get,
Acceleration cause relativity of simultaneity -> Relativity of simultaneity caused the resolution to the Paradox
So it would be like, Acceleration -> Relativity of simultaneity -> The resolution to the Paradox
If this is the cause sequence how can you conclude your statement with, "he root cause is relativity of simultaneity"??
Isn't it the "Acceleration" which is the cause of the relativity of simultaneity should be the root cause?
I consider the paradox solved the second she changes velocity. As soon has that happens she can no longer consider herself at rest and the brother as the one moving. That breaks the constant velocity rule that is used to create the paradox.
Very thorough explanation.
Another way to understand the phenomenon is though the space / time plotting. In the space / time plotting the path taken by the two space ships is that of two segments of lines and that of earth is one segment of line and the three segments connect on the meeting points, creating a triangle. Now the fact that more time passed for the spaceships comes directly from the fact that the sum of length of two sides of a triangle (the time passed for the two spaceships) is always greater than the length of the third side (time passed on earth). Thus all comes down to the triangle inequality in this specific scenario.
Less time passes on the spaceships.
In spacetime, the "straight line " is the path of longest proper time.
Mind blown! Excellent stuff!!!
I still don't understand but I came up with another version that I can accept. Consider the spaceships both have a camera recording Earth and there are really these gigantic numbers on Earth's surface as the clock ticks, then from the 1st spaceship perspective, because it is moving away from Earth, it sees these number images changing slower than its clock (like 1~2~3~4~5~). By the time it reaches the planet, it only sees 5 from Earth, while its clock is at 10, but the clock on Earth is already at 20 (just that the number 20 image hasn't traveled to the spaceship yet). The 2nd spaceship perspective, it also sees 5 from Earth when it is at the planet, but because it is moving toward to Earth, it sees these number images changing faster than its clock (like fast forwarding from 5 to 40). By the time it reaches Earth, its clock is at 20, but obviously it sees 40 as the same as the clock on Earth is also 40.
It is the best I have seen, but still not enough! Physics cannot understand what people do not understand. There are so many videos because no one has explained it well.
No one cares about the return. People think like this. When twin A sees (or thinks) twin B reach the star, he is frozen, and when twin B sees himself reach the start, he is frozen. Each thinks the other is younger. When they meet, when we compare the frozen bodies, which one was right? I know the key is simultaneity, but this is what you have to explain. What is the mistake of the moving twin?
Forget about the return, nobody cares about the return. How can you theoretically not see that nobody cares about the return, and you just explain the return. It is unbelievable. It looks like they are avoiding something.
As we can see above, the key of the difference is not either the acceleration or the changing of system, but that one has "moved inside" the other (reference point of the journey were all of one system).
Let us imagine the moving twin comes with a star after him (with the double of proper lenght of distance). When he reaches the fixed star he thinks that the other star did not reach the other twin, and fixed twin thinks that it has just reached him. (g=2)
Fixed twin calculates things based upon his reference system and the fact: when he SEES MY star (at distance 0) and at the end e corrects the time. The same result (age for the fixed twin) is given if the other twin does the same. He knows that the other twin is going to commit suicide when he sees the moving star (at distance 0). If he calculates the time for the star to reach his twin (according to his reference system) he gets the same result (4x1/2=2). The all problem is non simulataneity and reference points (lenght contraction).
"But where is the asymmetry?" people ask. In relativity, there is no such thing as a point in space, only points that belong to a reference system (if you understand this, you'll understand everything). The asymmetry becomes clear when events happen at points that belong to the reference system of one twin, but not the other. Changing reference systems and acceleration are only side effects of this, not the cause as we proved above.
I'm still mulling this over. I think I understand how it resolves the paradox with the two ships, but one thing I would like to see is how this reasoning resolves the original twin paradox.
The correct answer is that both twins are the same age as they experienced the same amount of time. One just experienced more space, as shown by the difference in clock readouts.
What is never mentioned is the fact that both clocks used the same amount of energy and had the same amount of run TIME.
Nor is it mentioned that the atom is being chilled to absolute zero and shielded from electromagnetic interference. The observer would have to be in cryostasis and wearing sunblock to be in the same TIME frame as the clock.
Space and Time are separate frames of reference. The paradox arises because someone combined the two together and foolishly believed that clocks measure time.
E=mc. Mass is stored energy, c is the speed of light, which is acceleration. Time is the measurement of acceleration, so E=t or Energy equals Time.
Both clocks used the same amount of energy, so they experienced the same amount of Time.
How much energy did each twin use? Its not given, so the correct answer is they are the same age.
Nobody here departs and returns. Like the twin paradox. You should do a video on that.
Why can't we just do the original set-up and just count clicks adjusted for doppler in each frame. Then we would know how the home twin experiences time during our constant motion and our acceleration.
Someday we will have the technology to send light signals and the mathematical tools to compensate for the doppler. Then we will truly solve this paradox.
I don’t understand what you mean by being able to “feel” acceleration. You can feel it if the ship is pushing on you, but what if you and the ship was accelerating due to a nearby star. In that case wouldn’t you feel weightless despite accelerating towards the star?
There are too many things wrong in this resolution to go into. Let's just say this: If this "resolution" were true, physics no longer has an explanation of the Michelson-Morley experiment, for the "length-contraction" of the apparatus arm in this experiment is considered only a measurement effect - like measuring your toaster with two rulers of the same length, but one marked as 12' and one as 6" long - so a "contraction/expansion" of the toaster based purely in the screwy rulers - a measurement effect (in SR the "rulers" are light rays and synchronized clocks or unsynchronized [depending on whether the observer is considered moving]). In this "twins" resolution, length contraction is being taken as a very real, very physical effect (NOT as a measurement effect), just as time-dilation is also being taken as a very real, physical effect given the twins are indeed aging differently - youthful skin versus grey beard. In SR, the two effects (time, distance/length) MUST be of the same order, for the Lorentz equations, in Einstein's system, are compensatory - length contraction trading off for time-expansion. - and this "order" must be that of measurement. To save the explanation of Michelson-Morley, the length effect MUST be considered a measurement effect (Lorentz's original theory of a very real, concrete "contraction" of the arm parallel the direction of the ether "current" was rejected in favor of SR) - and any time-effects (and indeed these are very physical, very real - clocks slowing, muons living longer) require a different explanation than SR can provide given its logical structure (which can only treat things in terms of measurement effects).