Why Solutions to the Twin Paradox are WRONG

Do "solutions" to the twin paradox leave you confused or skeptical? You're not alone. An examination of three popular YouTube videos pinpointing where and why they get it wrong. Plus, Albert and Emmy get chatty.

[ScienceClicEN]

Great video, I agree that the paradox is all about the absoluteness of acceleration. I would tend to say however that acceleration *is* absolute in relativity (as opposed to Newtonian mechanics in which it is simply relative). To me that's precisely the answer to the paradox : acceleration is not relative in relativity, one of the spaceships accelerates more than the other, and hence comes back younger than the other twin. You can simply measure it with an accelerometer in each spaceship. And by integrating the acceleration measured by both accelerometers, you can tell which spaceship has accelerated the most, and hence which of the two twins will be younger. You are right though that the "solutions" usually don't tackle this subtelty which is in reality the whole core of the paradox : how do you know which of the two spaceships has truely accelerated ? This is answered through the notions of geodesics, and in my opinion this paradox is perfectly designed to show how spacetime in relativity has an intrinsic metric (the youngest twin is the one who has travelled the shortest path), as opposed to the purely abstract coordinate description of spacetime in Newtonian mechanics.

[johnschultz]

Sorry, but actually THIS explainer is wrong. There really isn't a paradox and your anti-solution is incorrect.

If we adopt your preferred example where the twins move away from each other but then eventually turn around and return back to their origin, then obviously there is an inertial frame that makes all of twins' movements entirely symmetrical. In this frame, BOTH twins do NOT maintain their inertial frames as they move. Certainly at their respective turn around points, they both deviate sharply from what had been their previously inertial movement. If there were free floating oranges in their rockets, then when they turned around those balls would have all splattered against their walls. You can draw the space time diagram and regardless of what INERTIAL frame you choose BOTH twins will have kinks in their world lines. Neither of them maintained inertial movement! If they experienced the same forces/accelerations in the origin's inertial frame, then they will have both aged the same when they both return to the origin, but less than if a triplet had remained at the origin.

Now, you will argue, but all motion is relative! Can't we simply adopt the frame of reference of one twin (and then the other), claim the other twin is the one who is moving, and then come to contradicting conclusions? The answer is, no, you can't actually. It comes back to inertial frames. With the twins relatively moving away from one another and then coming back together again, then at least one of them (and possibly both of them) must have gone through some non-inertial motion, which people variously call a change in velocity, acceleration, forces, frame switching, etc. Furthermore, we CAN measure in an ABSOLUTE sense which of the twins experienced (more of) that non-inertial motion by having them carry accelerometers. If one of the twins' accelerometers stays at zero the whole time, then that twin is the one who maintained their inertial frame and the other must have deviated from theirs.

But all of that is largely besides the point. The real answer to the Twin "Paradox" has to do with in which frame of reference you ultimately do your final clock/age comparison. If you declare the "stationary" twin as the frame of reference in which you will ultimately compare and that twin experiences no non-inertial motion (i.e. - their accelerometer constantly reads 0 throughout the scenario), then we know that clocks in that frame will run fastest in SR. Any clocks that are moving relative to that frame will run slower, no matter how they move. So long as the moving clock ultimately comes back into that same frame (i.e. - their relative velocity becomes zero) and the clocks are then compared in that frame, then the stationary one will have ticked the most.

[lancebradshaw]

This has been said before in the comments, but I want to reiterate that acceleration is not relative. Alice can't say that she is sitting still while Bob is accelerating or vice-versa. Both of them will know that they are in an accelerating frame. It will produce a force that can be detected. That will let them know that neither of them are in an inertial frame. So special relativity is insufficient to give you an answer. General relativity must be added. If both of their clocks were synchronized before they started accelerating, both accelerated at the same rate in identical ships for the same duration and both turned around after the same amount of time, then the situation is perfectly symmetrical and Alice and Bob will both age at the same rate. The situation has to be asymmetrical in order for one person to age more quickly than the other.

[oldjoec]

The accelerating participants in this thought experiment ABSOLUTELY know they are accelerating. They feel the force of acceleration, and they can see that there is no source of gravity. So, ithey have all the data they need to know that they are NOT in inertial frames of reference. The premise of your objection (and therefore your entire video) is wrong. The frames of reference are NOT interchangeable, as they would be if they were inertial.

[mathboy]

I can appreciate this video's confused mistake - it's perfectly natural to imagine that the twins are in a perfectly symmetric situation, and that each twin should be able to declare that it's the other who's motion is changing, and that it's only thanks to reference to the stars or Earth or whatever that the twins aren't on the same footing. That was my first reaction when encountering this "paradox". But then I thought about it for a moment, and no, the twins are definitely not on the same footing.

Identifying a frame of reference doesn't mean you've identified an _INERTIAL_ frame of reference.
Twin B can make his frame the "he's at rest" frame, but it doesn't make it an _INERTIAL_ frame - and in fact it's not.
If twin B is in an enclosed room in his ship, with no view outside and nothing inside but him freely floating, then twin B will experience being slammed into some wall of the room at about the trip's halfway point as his ship turns around, and so twin B know that outside his enclosed room, either (Einstein's Equivalence Principle):
1. a gravitational field has been encountered (the ship containing his room has landed on a planet), or
2. the ship containing his room is experiencing an acceleration (equivalent to the ship's velocity has changed, equivalent to his ship-frame of reference is not an inertial frame of reference).
Meanwhile, twin A, who IS in an inertial frame, if kept in a view-less enclosed room, experiences no acceleration during his "trip" (being at rest, "moving" through time). Twin A doesn't fall into a wall of that room, but just floats the whole time.

[furia]

but it is super easy to say who is accelerating. To accelerate you have to use energy. so it is absolute.

[Mr.Not_Sure]

Your mistake is at 7:04. Not "all frames are equal", but "all inertial frames are equal".

[cameronconrad]

This video is actually incorrect. It states that acceleration, and therefore inertia, is not absolute. But while time and length are relative, the laws of physics (which includes inertia) are absolute.

[AvinashSPhysicsMathTutor]

Mistake in this video #2. The video considers a symmetrical version of the twin paradox in which both spaceships move away from each other, take a turn, move towards each other and come back to near each other. It says that this cannot be explained using acceleration because both are accelerating relative to each other. Correct answer is this can be and must be explained using proper acceleration. When the spaceships are moving at constant velocity relative to an inertial frame, then each observer will see that the other observer's clock is slower. When the spaceships are accelerating (proper acceleration), then according to General Theory of Relativity, each observer will see that the other observer's clock is faster. The net result is that, at the end of the journey they will agree that their clocks recorded equal time durations.

[EduIreland]

Acceleration is not completely relative. If Alice accelarates, energy needs to be used against her inertia to cause such acceleration, and if the only other object in the scenario is Bob, the only options Alice has are to either push against Bob, which will cause him to accelarate in the opposite direction, or Alice can push something she has on her ship (usually fuel) in the opposite direction of her acceleration, in which case, she also loses mass.
In both methods, the acceleration requires another element (Bob or fuel) to which Bob accelerates against.
Also, the acceleration will only last while there is contact between the two parts, the moment that that contact ceases, so does the acceleration and now the two entities are moving away from each other at a constant velocity.
Finally, in the given scenario, when Bob decides to turn around, they either need to interact with another element or spend some of their own mass in order to change their velocity, while Alice doesn't, which is then not symmetrical anymore.

[runepedro]

There’s no way to pick a preferencial frame of reference between two objects in Uniform Linear Motion and that’s it. It has nothing to do with an accelerated object. In the scenario where one twin is left on Earth, that one is the one with zero acceleration. The other would notice it has accelerated and there’s nothing in special relativity which contradicts this.

[peterrobinherbert]

And the maker of this video doesn't understand relativity. There is something that can tell which twin is accelerating because as he is accelerating he will see light curve whereas the stay at home twin will not see the local light curve. It is not a symmetric situation. As I said earlier the twin paradox is not even a paradox, its just counter intuitive. It is perfectly consistent. The math works and it has been confirmed experimentally.

It doesn't need a solution. There is no problem to solve.

[Paradoxolog]

Acceleration isn't relative. You can't just confidently say you're at rest while the other plane is accelerating, while your favourite tea mug is flying backwards towards the wall.

[rxotmfrxotmf]

The statement that you do not know which twin is accelerating if you remove the background is wrong. We DO know which twin is accelerating. Einstein stated so himself: the frame that experiences a force is the frame that is accelerating (his famous example of an elevator accelerating at 9.81 m/s^2 is indistinguishable from a stationary one on the earth's surface), and the frame that experiences no force is inertial. So the twin that turns around first has to undergo negative and then positive acceleration, where a force is experienced during any acceleration. For that twin, time slows down.
If both twins go in opposite directions, turn around, and return to their starting positions in exactly the same way, both their clocks will have slowed by the same amount relative to a clock placed at their starting (stationary/inertial) point, but both twins' clocks will still be synchronized with each other.

[Raptor]

But don't you need to expend energy to accelerate? A change in direction at a constant speed also counts as an acceleration, but presumably you also need energy to change direction? It may not always be apparent to observers who is accelerating, but the universe is keeping track. Whoever is expending energy is the one accelerating.

[jarnold]

You are mistaken. Acceleration is objectively different from being "at-rest." If you are in a spacecraft that is not accelerating, a ball will float freely inside. If your spacecraft accelerates, the ball will move to a wall opposite of the acceleration, and will press against it for as long as there is acceleration.

[khimhernane]

I respectfully disagree
An accelerated frame can be distinguished easily. It is absolute. Only velocity is relative in this case.

It comes down to the two postulates of SR. Especially the first postulate. In an inertial frame all laws of physics is the same. Therefore, once in an accelerated frame the laws of physics won't hold. This why it is distinguishable. If in some way we observe that a law of physics does not hold in your frame it is an accelerated frame.
So if im in a closed box in space without windows and I dropped one of my tooth to the ground if I observe it to just move horizontally away from me. I know a physics law is broken so I must be accelerating. If another person in a different box happens to observe this occur to me, he can also say that I accelerating.

All im saying is that an accelerated frame can easily be determined.

[Kuvina]

Hello dialect. I discovered your channel through your tensor video, and I think your videos are great! Although I will admit I'm slightly bothered by your accusatory tone in this video, I can see that you have clearly changed to a more respectful tone in your later videos, which I definitely appreciate. I have a bit of a question though. I know this is a long comment, but if you would read the whole thing, it would make my day, and I really do think it's important, so if you do choose to read it all the way through, thank you so much.

The paradox that you introduce is one in which there is nothing in the universe other than the 2 observers, and the only thing you know is that they both see the other one accelerating. In my experience, this is not the same as how I have always heard the twin paradox. I've always heard it where you do have other objects in the universe (like the earth) to base motion around. This is also the way that most explanations introduce it. Something that you didn't mention is that a lot of these explanations also mention the fact that this version is not a true paradox. So your version is a paradox, and so it's unsolvable. The version most explanations explain is not a paradox, and so it is solvable. Because of this, I think this whole controversy is just a debate about semantics. Yes, acceleration is technically relative, but by adding other objects to the universe, you gain something to base acceleration off of, making it, for most intents and purposes, effectively absolute. In this way, acceleration (or change in inertial frames, whatever you want to call it) both does and doesn't solve the twin paradox. If you make acceleration absolute, then it does solve the popular version of the paradox (which isn't actually a paradox). If you acknowledge that acceleration is not absolute, then it demonstrates how your version of the paradox can't even be solved in the first place (making it a true paradox). For that reason, I think that solutions to the twin paradox are not "wrong" as you say, but they just don't solve the same thing that you consider to be the "only true" version of the twin paradox. In other words, the only way to actually solve the paradox is to make acceleration absolute, or to make something else absolute. In one of your later videos, you mentioned that it's not acceleration that determines time dilation, it's the curvature of space time. Yes that's true, but then doesn't that mean that spacetime itself is now absolute? The only way for it to be a paradox is if spacetime isn't absolute, like how you state in this video's introduction, in which case you don't have enough information to know what the curvature of spacetime looks like. In the case of flat spacetime (the way the paradox is almost always given), it would seem that the measured acceleration from an accelerometer does in fact give you enough information to resolve the paradox. So even though acceleration technically isn't relative, for all intents and purposes (at least in the context that the twin paradox is almost always given), it may as well be. That's why I don't think it's an issue to consider acceleration to be absolute, and use that to resolve the paradox. By stating how you have the earth as a reference, and that it's not really a paradox, these explanations are saying that their version of the paradox is solvable, which means that it's reasonable to treat acceleration as absolute. I think it's important to acknowledge that just because an explanation doesn't go as deep as possible, it doesn't mean it's wrong. Just because something is not perfectly accurate, it doesn't mean it's not a useful model. And by the looks of it, the vast majority of people are content with these explanations. Just like how classical phenomena can be explained by a gravitational force, even though gravity isn't a real force, and is instead just the curvature of spacetime. The notion of causation is purely semantic in nature. These videos are not meant to take a deep look into theoretical physics, they're meant to explain science concepts to lay people, and in that aspect, I think considering acceleration to be absolute is a perfectly reasonable thing to do. So now I just want to ask: why are you so passionate about hating these videos when they're so clearly just explaining a more popular version of the paradox to the general public, without needing to go so deep into it? In my opinion, a lot of them succeed in this goal, and there's no reason to fault them for it.

[frankmuennemann]

I don't understand why this video hasn't been pulled down. It's claims are simply wrong.

[noname-sgqx]

I disagree with you on the part where acceleration is absolute, the thing is when ever you are accelerating like in a car or something, then you feel a force, now heres the thing with Bob and Alice, suppose its Bob who reversed the thrusters, to Bob it may look like Alice is coming back and to Alice it may look like Bob is coming back, but in fact Bob can confirm that he is the one who truly accelerated, since he is the one who felt the force, for Bob it may look like Alice is coming back, but Bob felt the force, and Alice didnt, so basically the acceleration of alice is fake