Why Solutions to the Twin Paradox are WRONG 

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.

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.

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.

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.

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

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.

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.

Sorry but unfortunately that's wrong. Yes you can absolutely measure the acceleration through inertial forces. You can very well feel that force during e.g. take-off of an airplane while everyone at the ground will not. And yes you will also feel that without the planet around because that's due to the acceleration and not Earth's gravity. Actually the twin problem can also be explained without the acceleration from earth (or whatever fixed point) as long as one knows who's turning around and traveling back to the initial position and who's been at rest at that point. Also the symmetric attraction/repulsion you've been talking about in the end is Newton's mechanics and not relativity...

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

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.

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.

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.

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.

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.

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

The mistake this video makes is that it tries to apply concepts of special relativity to non-inertial reference frames (reference frames that accelerate). Once non-inertial reference frames start being used, special relativity is no longer accurate; you need to use general relativity instead, which nowhere near as simple as reference frames are in special relativity models. That is the "true paradox" in the twin paradox: trying to explain the behavior of an accelerating reference frame using special relativity, which doesn't include accelerating reference frames. In short, acceleration isn't relative in the same way that velocity is. Velocity can be interchanged between reference frames, but acceleration cannot. If I were falling toward the Earth, my acceleration would be about 9.8m/s^2, which is completely fine. However, if the Earth were accelerating toward me at 9.8m/s^2, then at the low speeds we're travelling at, the force causing the acceleration can be closely estimated by F=ma. Given the Earth's large mass, there isn't a force large enough to bring about such a large force. In any inertial reference frame, the Earth and I could be seen as accelerating towards each other, but my acceleration will always be much greater than the Earth's. Likewise, if one of the twins never turns his or her rocker on, then there is no force applied to the rocket, and it cannot be accelerating; instead, it is the other twin's reference frame that is accelerating. The twin paradox has been physically tested through comparing atomic clocks on airplanes with atomic clocks in labs, and the clocks on the planes have returned slightly behind those left in the lab. General relativity completely accounts for this difference in both the lab's inertial reference frame AND the plane's non-inertial reference frame.

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.

the one who accelerates must feel a psudo force where as the one who does not accelerate dont feel it.does this break symetry of the problem

Unlike velocity, acceleration is not just a relative concept. In fact in your example of only two rockets being the only two objects in the universe you know you are accelerating when you turn the rockets on and your face starts deforming and your back pressed against your seat vs when you turn the rockets off. That is Einstein’s equivalence principle.

Why can't acceleration be absolute when you have two ships? You can always measure the change in velocity of a ship to its pilot, which gives you an inertial frame to reference from. Dropping something within the cabin while accelerating also does this. As mentioned in every video you referenced, the dialation is clear based on the spacetime path taken. The spacetime diagrams illustrate this, but you've decided to ignore it. Weird video, its misinformation and the humor is sexist.

Except acceleration IS an absolute. All observers in all inertial frames of reference will agree that the twin in the rocket ship is the one who accelerated. They can even measure their own subjective acceleration through use of an accelerometer. That's the asymmetry.

Acceleration is absolutely not relative. The object that is accelerating is the one that turns matter into energy. If there are two identical rocket ships speeding away from each other, the one ends up with less fuel is the one that has undergone more accelaration.

But acceleration IS absolute! You can measure it and know which of the two ships is accelerating. Using an accelerometer you can measure your acceleration. And if your accelerometer reads nothing and a spaceship standing still 1 km away starts accelerating towards you, you know that it is accelerating and not you.

Who is accelerating is obvious. The one who burns fuel is accelerating.

7:13 Neither apple nor earth accelerate in your example. Free fall in gravity field is not an acceleration. Acceleration would happen if apple was on earth surface and couldn't free fall any more. You are mistaken about one important thing. In special relativity accelerating frames differ compared to inertial ones. Velocities are relative but acceleration is treated as ABSOLUTE.

Huh, really? My understanding is, that acceleration can be measured locally. So Alice could know, if she's accelerating or not. I claim, that there's no twin paradox, if both are accelerating in opposite directions and come back to the same location. The twin paradox happens, if one is for example not accelerating and the other is, and this difference can be measured.

No... There is a difference. The acceleration produces a counterforce equivalent to gravity. Each observer has the reference of their own inertial acceleration to compare to their visually apparent acceleration away from each other. By comparing the rate they appear to be moving away relative to each other to their own G-force, each can determine independently of each other, which of them is accelerating, and at what rate. This is true if both accelerate, if either accelerates, and if they both accelerate at different or similar rates. If both accelerate away from each other and then return, there is no paradox. Their clocks BOTH slow by time dilation according to their own rate of acceleration and those rates of acceleration are independently discernible. When they reverse their course and return to each other, the age of each will be a matter of the time dilation each experienced, and that will have a measurable dependency on the G-force generated by the acceleration of each, independent of the other. If they experience equal g-force, their clocks will slow similarly and each will have the same net time dilation. If they experience different g-forces, each will be able to predict their aging difference on return by comparing their visually apparent acceleration to the g-force they experience. If one remains stationary while the other accelerates away, the stationary observers clock may appear to the accelerating observer to slow down, BUT if it's compared to the G-force generated by acceleration, the accelerating observer will be able to correct this and deduce that it is his own clock which appears to him to tick quite normally, that has slowed. If gravity wells are involved, then it becomes an n-body problem with the time dilation effects from each source of acceleration force accounted over the duration of the trip at whatever rate of change to that G-force that each experiences. What is important is not whether they are in relative motion. What is important is acceleration. An observer on a relatively stationary planet still experiences acceleration from planetary gravity, and so does the traveler leaving the gravity well on their trip away from the stationary observer, BUT the traveler has an additional acceleration which both observers can independently verify as unique to the traveler by the additional acceleration force experienced only by the traveler. Regardless of what other bodies become involved in the problem, it is the acceleration forces imposed on both observers that produce the temporal effect each experiences. The observer experiencing the highest acceleration (and g-forces) will experience the largest time dilation effect.

Wow, this is completely wrong. Acceleration *IS* absolute because the force that causes it is absolute. We know from Newton's laws that things accelerate when and only when they're acted on by a force, and we know from relativity that causality is the same (not relative!) in every reference frame. So in both of the twins' frames, their acceleration away from each other is _caused by_ a force on just one of them (e.g., one of their rockets firing, which only that twin can feel), not just correlated with that force. And note that the traveling twin doesn't have to accelerate all the way back to the earth in order to age less than their sibling. For example, if they fly away from earth for 5 years, instead of turning around and flying back for 5 years, they could just continue away from the earth for another 5 years and then "stop" relative to the earth so that they're back in the same frame of reference. Then both of the twins' ages would be the same. It would just take longer for them to verify it with each other (since they'd have to send signals to each other from light years away), but they would certainly come to an agreement on their ages. "The whole point of relativity is that there are no preferred frames of motion". No, the point of *special* relativity is that there are no preferred *inertial* frames of motion. Accelerating frames are *not* inertial. And the point of general relativity is 1) that accelerating frames are equivalent to those that are stationary in a gravitational field and 2) that inertial frames in flat space are equivalent to those that are free falling in a gravitational field (curved space). Therefore, claiming that the question of who's inertial and who's accelerating in flat space is relative is like claiming that the question of who's free falling toward the earth and who's standing on the earth is relative. Would that make any sense? "Alice and Bob won't agree on who is older" after they've reunited? Um, what?? What if one of them ages 50 years (while the other only ages 1 year) and dies of old age right after they reunite? And/or what if the spaceships are equipped with stopwatches? Would there be any disagreement then? Of course not! The amount of time that any person, clock, or other system has been subject to is an absolute fact, not a relative one. A few minutes on the relevant Wikipedia page should've allowed you to realize most of this yourself before spreading questionable info (not that it gets everything right; e.g., it downplays the critical role of force and acceleration). en.m.wikipedia.org/wiki/Twin_paradox Note: An older version of this comment incorrectly said that transitioning through different reference frames and rotating planes of simultaneity were causally more important than acceleration.

Why is there a paradox in the simplified model? We could say Bob needs to do something to turn around, in order to turn it has to do something e.g. throw some mass in the non Alice direction. That breaks the simmetry.

It's so silly. He claims that the twins have to somehow agree as if it's some arbitrary thing, but even without an earth, the rocket twin can do experiments inside his ship that prove just to them that they are definitely not in an inertial frame of reference for the entire trip, while, at the same time, if someone just on earth without reference to the rocket ship, were to make the same experiments, they would determine they are in an inertial frame of reference. That's the assymetry

Thanks for making this. I was always bothered by those other twin paradox videos too. I'm glad I'm not the only one.

I think we've all experienced the feeling of acceleration, so it should be pretty easy for Bob and Alice to figure out who is accelerating and who is not. Acceleration is not relative.

I don't see a problem with absolute acceleration. Acceleration *is* absolute in special relativity. We can also measure acceleration with an accelerometer and that measured acceleration is absolute (unlike, say, velocity or position). You have argued that accelerometers need to be calibrated and whether they're calibrated in an inertial or accelerating frame changes the result. However, as shown by the channel "Physics - problems and solutions" in a video titled "Is Acceleration Relative??? Dialect is WRONG!!!" you can, at least in principle, calibrate an accelerometer such that it can detect acceleration even if that acceleration is the same as it was calibrated in. I also know that you have seen that video since there's a pinned comment by you under that video.

You are very wrong because acceleration is absolute, you can tell if you are accelerating without reference frame. Relativity, classical Galilean or Einstein is about INERTIAL REFERENCE FRAMES, wich are the ones NO ACCELERATING. Those are the ones that are indistinguishable and there are note INERTIAL preferred frame. Accelerating frames invalidates all results both in Galilean and Einstein

Relativity says " one inertial frame is not preferred over the other."...you changed that statement and conveniently omitted the inertial frame part. The minute physics video is the correct explanation...

What breaks the symmetry is the FORCE the rocket twin PERCEIVES upon firing of his rockets! The Earth-twin or other platform-twin DOESN'T perceive that force. Variables are "perceivables". Space, time, velocity are perceivables equaly as FORCE is. The Earth twin perceives space, time and velocity, and the rocket twin perceives all the three, and force in adition to them! So, the twin paradox outcome boils down to the question: "Who is subjected to force and in which measure/amount (time/path and intensity of action)?" The answer to it will determine who will be younger upon reunion. We neglect the Earth's gravity effect on time passage and the Earth has a "free fall" from the standpoint of the rocket-brother at the very moment he gets subjected to the propulsion (he also moves out of the zero reference frame determined by the center of total mass of the cosmos, breaks it whereas the earth remains in it)

I disagree. The person is experiencing force while accelerating. The one on the earth does not experience force

Why wouldn’t all observers agree it is the space traveling twin that really accelerates? From earth, as the space traveling twin accelerates I would be able to see this. Everything in the ship would be affected by the acceleration (nothing would be freely floating anymore for the duration of the acceleration. The person in the ship would see this, so would the person on earth. The person in the ship looking at the person on earth would not see any change in acceleration of the person on earth. That is as they look at the person on earth as they reverse direction, the dropped apple would still accelerate to the ground at 1g. So yes acceleration is absolute. The person in the ship could do experiments that show he is accelerating and the person on earth could see the results of those experiments. The person on earth, while the rocket is accelerating could do experiments that show there is no change in his acceleration and the person on the rocket could see this. They would both agree who is accelerating. Is this wrong?

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.

Yet "firing" my rocket is a physical fact. And all agree on such events in relativity. Kinda the main point of the theory, not that everything is relative. Taking the stars and earth away isn't going to change that event. Relativity is an invariance theory. There is one solution, someone is younger. As for acceleration...did you get up this morning and think you were floating in space? Or did you understand you were still on earth? If so, then you detected acceleration.

Didn't Einstein have great respect for Noether, much like everyone else those days? I find that "Shush, the men are speaking" very inappropriate if so, as I'm pretty sure she was in his circle of friends, and might have even had his help emigrating (she was a Jewish German in the 30's), although I might be confusing her with Gödel on that detail.

In both special and general relativity, acceleration is absolute (the free falling object is the inertial one btw). Distance, position, speed and velocity are all spatial relationships between two objects and cannot be measured on a single object (because they are all between objects). None of them would have any meaning in a universe with only one object in it. This is not true for acceleration. If there was only one object in the universe, we would still be able to measure it’s acceleration. Actually, if there was only one object in the universe, it would not be able to accelerate. An acceleration requires a force. A force is always between two objects with mass and influences them equally, but in opposite directions. The total change in momentum in an isolated system is always 0. If you consider all three objects; alice, bob, and the mass that has to accelerate away from bob for him to turn back, the problem is no longer symmetric. If they both turn around and accelerate back it becomes symmetric again (now there are four objects), but in this case there will be no age difference between alice and bob. The paradox is apparent only, and requires a misunderstanding or obfuscation of special relativity.

You have neglected the fact that, for the object to be accelerated, a force must be applied resulting in an expenditure of energy. The other obect may 'appear' to accelerate relative to the accelerating object but there is no force applied.

As others have noted here, you CAN tell which of the two rockets accelerates. If you seal a human inside each rocket with no windows etc, you can detect which rocket undergoes acceleration entirely within your sealed room (using any number of simple methods, including just "feeling" the rocket accelerate). This breaks the supposed symmetry and resolves the paradox. If BOTH rockets were to accurate exactly the same amount, then BOTH turn around and return to the same point neither twin would be older than the other.

I think acceleration is absolute...

Acceleration is absolute - an observer "feels" the CHANGE in velocity regardless of what he or any observer thinks the relative velocity is. That said, these solutions should compute the age differences using general relativity, not special. The effect would be much less. However there's still a paradox. Take 2 ships with identical flight paths apart and back together (same acceleration / deceleration etc.) Who's older? Intuition says they'll be the same age, but I don't know how to show that using SR.

You say these other videos are all wrong, then claim that acceleration is not absolute? It is absolute; I don't need to look at fixed stars to tell whether I'm going faster or slower. In the Earth's gravitational field I am accelerating even when standing still on the ground. An object in freefall is not accelerating.

In the beginning of the video you have a screenshot from Fermilab. But, you didn't address his video. Science Asylum has a video too. Both of them say thee time difference is because the "traveling twin" has 2 inertial reference frames, distinct from each other. And even though they point out the acceleration on MinutePhysics, Henry says that the time difference is from the traveling twin having two inertial reference frames.

This is just wrong - in fact the previous 2 I just saw in this series are wrong too. These videos are just confusing people even more. Objects do not need to be physically moving with relation to each other to experience different time at all. It's about acceleration. So if you have 2 clocks and place one on the ground and another up Mt Everest, they will experience a constant recalibration in time - even though they have not moved in relation to each other. This is because of the time dilation caused by the acceleration of the earth's gravity - even when they are NOT moving in relation to each other.

Acceleration in flat space time is absolute. If you keep a filled water glass in the spaceship the water will spill out of the glass while changing velocity. No matter which frame you look from. The spilling of water defines the non-inertialness. The water of the glass kept on earth frame wont spill out. (Even if you remove the gravity of earth). Because its inertial. (Not accelerating). Conclusion: the frame whose water of glass spills out, will be the one who ages slower. If both glass(of two accelerating spaceships) spills water then the symmetry is conserved, otherwise not!! There is no absolute rest frame. But your own frame is the "special" frame, not the stars situated far away from you!! (Stars are not ethers and no ether exists. 😂)

Sorry, but I believe that 1:33 and 1:49 are incorrect. Neither Alice nor Bob can say that they are stationary. They are both accelerating, and therefore not in inertial reference frames. I think that is where many students become confused with this. I haven't taken GR yet, but I assume that is where we get into more of the non-inertial reference frame stuff. You can't say that only one observer is accelerating in your example, because they both feel a force, which means (by Newton's second law) that they are both accelerating.

I liked your video on the Christoffel symbols, but this video wrongly accuses other explanations on RU-vid of being incorrect. There is absolutely an asymmetry between the two twins due to the difference in their acceleration, and this is what makes one twin age while the other does not. Special relativity does *not* state that proper acceleration is relative, it states that velocity is relative. There is absolutely an experimentally measurable difference between the twin who stays home in the inertial frame and the one who leaves on the trip, which can be measured by an accelerometer. When the acceleration occurs, it changes the lines of simultaneity of the accelerating twin such that the twin left behind will age very rapidly during the turnaround from the traveling twin’s point of view. Why do you object to this explanation?

I feel like I'm missing something here. Surely the twin that experienced acceleration, can claim that they actually felt that acceleration, whereas the other twin can claim that they did not?

Sorry, but no. You stick to Special Relativity, but once you leave inertial frames with constant speeds, and start to use acceleration and gravity, you're in domain of General Relativity, which is whole another story. And apple falling to Earth is not equal Earth falling on apple, because a) gravitational force accelerates apple much more than Earth and b) from the apple POV not only Earth falls on it, but the whole Universe, that's kinda strange and gives a hint who's actually falling.

The twin “paradox” is merely the hyperbolic triangle inequality and if a “solution” to it is “wrong”, then you should be able to tell us what’s wrong with the elliptical triangle inequality.

Wow. It's the first time i even understood, why it is called a paradox. The subtle reframing of the question makes all the difference. Thanks alot

Hi! Great video but I didn’t agree with your reasoning. Yes, it’s not possible to determine which of two bodies is actually accelerating in space when considering relative velocities alone. From Newton's second law, acceleration can be measured through an unbalanced force. So, body A at rest (or constant velocity) will not experience a force, body B will and so is accelerating. Hence, A is continuously in an inertial frame, whereas B only is for part of the journey. Due to this distinction I would suggest that each frame preferentially has a different experience.

6:37 Acceleration _is_ absolute in _special_ relativity. This is a well-known "philosophical defect" of the theory This follows from one distinguishing feature of the special theory: its spacetime comes with an _a priori affine (linear) structure._ This is what intrinsically distinguishes accelerated motion: its worldlines are not _straight lines_ in the global affine structure sense. This "God-given" affine structure was something that bothered Einstein himself and was one of the reasons he sought to get rid of it (he succeeded in doing so in the general relativity theory). That's why what you say at 7:00 is not correct in the special theory in which there are in fact intrinsically "better" frames distinguished by the global vector space structure. As I said, Einstein found this issue somewhat unacceptable and sought to "fix" it. 7:43 That's why this is again incorrect. Assuming the special theory, both trajectories again have well-defined deviations from straight-line trajectories and the difference (if any) between those deviations results in the elapsed time difference upon the reunion. In the general theory the spacetime metric is generated solely by those two moving objects and again their elapsed times are well-defined numbers. The only way you could be correct is if this configuration (only two small bodies in the universe) had non-unique solutions for the spacetime metric yielding an ambiguous answer. I don't know this from the top of my head although the uniqueness theorems about the Schwarzschild solution (only one object in the universe) seem to indicate otherwise. So the bottom line in the general theory case is that even if there are only two objects in the universe, the situation is _not_ symmetric because the spacetime metric (the shape of spacetime itself) is coupled to the motion of the two rockets, so there is a third very important actor on this stage.

I enjoyed this video because it helped me to see how great the minutephysics explanation is. Before I saw that video, I might have been confused by videos like this, but now I think you could sit down and work out what happens in the symmetric situation, including the two accelerations, and it will be a pair of consistent accounts.

THANK YOU! Exactly! I don’t know a lot of physics, but I’m always dissatisfied with all solutions to the twin paradox I’ve always watched/read. They always introduce asymmetry to their solution, which exactly defeats the whole point of the paradox: they’re supposed to be twins with identical relative observations of each other. So many physics videos have unequivocally taught me that acceleration is absolute (which I never understand). But even if it’s true, why can’t both twins accelerate with their own rockets? After all, symmetry is the whole point of the paradox, hence “twins”. So I always wanted to challenge those solutions, but never knew to whom. I’m glad there’s finally a video that directly addresses the question I’ve always had and validates that I’m not crazy.

7:44 - The answer is "reaction force". Neither bob nor Alice can claim they're at rest, if they experience *reaction force* that occurs when acceleration is applied to mass.

I can't believe how wrong you are about this. The "stay-at-home" twin is always in the same inertial frame. She knows this because Newton's 1st law is always obeyed. The "out-and-back" twin KNOWS he is not in a single inertial frame because when he turns around he can observe that the 1st law is violated, i.e., isolated objects in his frame accelerate. This is where the asymmetry comes from. It is fundamental to understanding the problem. Now if each twin moves apart, turns around and returns, the symmetry is there and each twin will have the same age when they meet (but less than someone who stayed on earth).

acceleration is absolute, not relative to other frame of reference. If you were in an empty universe in a space ship and fire your rockets you would feel acceleration while the exhausted gas would not.

Wrong. Both you and they are wrong. The resolution has nothing whatever to do with acceleration. The answer to the paradox lies in the spacetime metric. The proper time lapse along different world lines that join the departure event to the reunion event is different in general. Proper time is the time recorded on the traveller’s on-board clock (your wrist watch, or your “ticker” I.e. heart, and so is directly related to the aging process of the traveller). If the proper time lapse is different for two travellers that part company and then meet again, then the travellers have aged by different amounts. Your problem is that you are trying to explain the paradox from a space based perspective. Relativity can only be properly understood in terms of spacetime. The paradox arises from the fact that the verbal description of the situation builds a symmetry in the wording that does not exist in the actual physics. There is in fact no paradox when the physics is analyzed - the person whose world line has the greatest proper time lapse ages most. For a clear non-technical description of the correct resolution, see Penrose’s discussion of the paradox in his Road to Reality.

3:21 who else cracked up at the earth rolling away? like that's what I've always wanted to do

This video is wrong on many things. You can just learn math an calculate the proper time (what you measures in your own clock) that each twin has experienced on each situation: If one of them is the only one that accelerates, the proper time will be less for him. if both accelerate to depart and to return, they both aged the same. And acceleration is absolute in especial relativity: an observer can tell if he is accelerating or not (or at least believe that he is at rest but in the presence of a gravitational field, which we do not need to consider in special relativity).

Thanks for making this! Now I have another question though. Can't you also argue that the earth and fixed stars are accelerating and moving away from you at light speed? Maybe it's more to do with energy spent?

If we're going to say you can only measure acceleration wrt distant stars, then we may as well just return to Mach's principle and be done with modern physics. But firing a rocket necessitates that you experience acceleration. Alice and Bob follow different paths from point A in spacetime to point B in spacetime. In the usual scenario, Alice's path is geodesic (modulo a slight deviation due to Earth's and Sol's gravitational fields), while Bob's is not. In your modified problem, neither Alice nor Bob is following a geodesic path. The clue to that is that they both have to fire rockets in order to reach point B. So both will have shorter path lengths in spacetime than the geodesic path from A to B. If they undergo equal but opposite acceleration profiles, then they will age by the same amount. I think this video will only confuse people.

Even in the absence of a reference point in an isolated system those two spheres would still be subject to time dilation as per lorenz transforms (relative to each other as long as their average velocity is not equal)

Acceleration requires energy. The more a given mass accelerates the more energy it has. Whats the difference between the traveling twin and the non traveling twin? Energy. What distorts spacetime perception or energy?

hey, I liked your video and thought it was pretty good. I'm curious if you could develop a way to display how waves would affect time dilation on a 2-dimensional plane, thanks!

The assertion that because there is no absolute velocity, there is no absolute acceleration seems false. Because acceleration is a change in velocity, this "absolute velocity" is cancelled out. This clearly applies to newton, where any two "inertial" frames of reference will behave the same regardless of their relative velocities to one another. Velocity doesn't make any difference, but the change in velocity makes a great deal of distance. Can somebody weigh in on whether acceleration is arbitrary in the same way as velocity in the theory of relativity?

you are wrong. It is important who is accelerating and who stand still

You are misrepresenting what I said in my video. You claim that I said that both Adam and Sarah will agree that it is Adam who accelerated. This is not the case. I stated that Adam will believe that he was standing still during the entire journey, including during the time when he fired his rockets.

One twin gets crushed by G forces, the other doesn't. The frames are not the same. Both agree on who did the acceleration. Really confused by this video.

Your explanation is so profound because it is less concerned with the answer and more concerned about the exact problem. Humans tend to favor the former vs. the later because we seek the easy answer. Please correct me if I’m wrong, but I paraphrase a supposed quote of Einstein’s which I believe went something like, “if I had 60 minutes to save the world, I would spend 5 minutes on the solution and 55 minutes discovering the true problem”. Whether true or not regarding the supposed quotes actual origin with Einstein, it nevertheless profound and equates in my mind exactly to what you did in this video. Bravo and well done!!

Acceleration is absolute in the sense that you can equate not accelerating to moving along a geodesic of the curved spacetime (aka free fall). The absolute acceleration is then just the deviation from free fall.

You strated well but did not get anywhere really. Hope you continue on this. people talk about TWINS paradox as if it is an exceptional situation in SR. Well, it isn't. All of SR is about this situation in an infinite forms. The main probelm is to preserve the symmetry of motion in Inertial frames and undrestand the notion of time and space consistently. The notion of time vs. clocks, space vs. rods and the connection between Mathematics and reality is not so clear.

I just watched the same video by Professor Dave and I was boggled as well by his non-inertial frame of reference answer. So thanks for this.

I think perhaps the simplest answer to the paradox is that a comparison of the two observers' local elapsed times cannot be made, unless they area brought back together again. The details of how they are brought back together will determine their elapsed time comparison. But if they simply set off in opposite directions forever, the two viewpoints are symmetric.

Which reference frame is accelerating is absolute and relies on the net forces acting on the reference frames therefore which frame is accelerating is not relative. I do wonder of the outcome of the paradox in a situation in which both frames accelerate

I don't understand how there can be any question as to who is accelerating. If you accelerate you can feel it, and if you accelerate too fast, you die. On the other hand if you're not accelerating you don't feel it and also live. Does this not break the symmetry?

I visualized the same scenario about 2 space ships departing in opposite direction and then each applying a force to reverse their directions and meeting again. I had no idea if either one is older upon completion, and now after watching your video, I still don't because you didn't answer the question. If you don't know the answer, what's the point in criticizing other explanations?

Thanks for the video. I was not satisfied with other videos that choose a preferred reference and claim one twin accelerates

Thanks for this, mate. Very well explained and it cleared up a few things for me. Cheers.

Respectfully, I think you're wrong. We can measure acceleration and therefore both twins would agree who had a change in their acceleration/gravity. That's where the symmetry breaks.

How do you even define an inertial frame of refrence without the notion of acceleration? An inertial frame is usually defined to be one which doesn't have a force act on it, and hence has no proper acceleration.

what if the other twin travels at a constant speed without acceleration, she just goes straight away from the earth? Is there any time dilation effect? Or will she be younger? Really want to know

I hope that the author of this video had spent last couple years on more detailed studying of the subject so he would not confuse his viewers in the future videos with his false statements, flat, unrefined view of the concept, and misleading conclusion. For his scenario both observers must agree on the exact moments and time periods of actions on their "proper clocks" otherwise the whole experiment will fail, as they can not (physically) synchronize their actions during experiment by observing each other. Here we have - two observers (accelerating in equal time frame until same beforehand agreed speed has been achieved) and then moving away from each other with constant speed and then (after some beforehand agreed time has passed) turning towards each other (decelerating and then accelerating in equal time frame in the opposite direction until they both have same beforehand agreed speed) will both agree *at the moment of crossing* of each other at the point of origin (lets assume that it stays in the same place for the whole time) *on the time that has passed* since the start of the experiment *is same* for both observers. Remember about how Einstein clocks work, but with some additions. Imagine that clocks work like pulses each second traversing trough space with speed C. A stationary observer (or observer that moves *non accelerating* relative to the clock) will see a set of concentric circles evenly moving away from origin of time-pulse like this * (o) * (_ (o) _) * (__ __ (_ (o) _) __ __) If the source of the pulse or the observer move away from each other the interval between pulses will be observed as being longer because the length of space that signal must have to traverse will be bigger (i.e. if they are moving at constant 0.5c from each other, than the interval will be 1.5s between pulses) and vice versa, but they will stay the same . Moving away: * (__ __ (__ __ ( o> - Signals travel more distance and take more time to reach observer Moving towards: * (_ (_ ( - That looks like a "more sparse" space-time of events Accelerating towards: * (__ __ __ (__ __ (_ ([ o ] > [ o ] > [o ] Einstein had written something about that almost a century ago (object in free fall vs object in empty space) So in the scenario described in this video. Each observer will see the other as aging slower, while accelerating away, then aging at same speed while moving away at constant speed, then - aging faster, while accelerating towards each other, and finally - aging at same speed while moving close each other and also having same proper time that has passed since the start of the experiment. You can also get the same answer if you put third observer at the point of origin and do the math from his perspective.

While I agree that most of the videos out there are wrong, this video is crazy wrong. Acceleration isn't relative. More real acceleration? You do realize that alice and bob, since they both accelerated from each other will meet back and be the same age. By accelerating, they both left the initial frame and return to it. To make the example of bob and alice like the twin paradox, only bob or only alice can accelerate. One must remain in their original inertial reference frame. The earth and the stars have nothing to do with this. It has to do with one twin remaining in their inertial reference frame and the other twin leaving that frame and returning to it. It isn't that the acceleration itself is causing the difference, but it is required in order to move between different inertial reference frames. Thus, the problem isn't symmetrical like people think.

From the premise that they start at the same location and ends up at the same location, Bob know that there was a an acceleration because he could feel it. Alice can deduce it on the premise that the start and end up at the same location. She knows that in order for Bob to return with a velocity different from when he left, there had to (be at some point) an acceleration. Thats why both obersvers can agree on that Bob has exprienced an acceleration, and thus aged less.

Hi Dialect, good video and very thought provoking. Some of the comments here saying you changed the experiment is totally missing your point, which is that the reference frames are identically symmetrical. But I think it is possible to differentiate between the 2 rockets, which one is accelerating and which one is not. In non-inertial reference frames, all frames are equivalent. Not so for accelerating inertial frames. The actual stationary rocket (the one that did not fire the booster) feels no “force”. If a person was “floating” in the middle of the cockpit in the middle of space away from all gravitational fields, he or she will remain floating during the whole of the experiment. On the other hand, the person in the rocket which fired its boosters will feel a “force” and if he/she were floating would actually move to the back of the rocket and be pressed against it. In this way you can see that it is not symmetrical and the two reference frames are not the same. I think that “force” is equivalent to gravity and will slow time for the rocket that fired the booster and cause him/her in that booster to age less, that’s where the missing time went.

When the rocket ship accelerates, you would feel acceleration as your own speed would be instantaneously changing, _relative to yourself._ - It is you who feels acceleration and not the people on Earth or _any_ part of the university. --- So this is a distinction between Object A and Object B. Likewise, an apple falling down would not experience any acceleration, rather it is the Earth accelerating towards the apple. You don't feel acceleration when you are freefalling, but you do feel acceleration when you are standing (i.e. your own weight) or in an accelerating car.

I see ur point but it is still correct to say the person in the rocket ship is the one who accelerates bc they feel a force which causes them to accelerate. The person on the earth is at rest the whole time in their reference frame and remains in an inertial reference frame, while the rocket ship man doesnt

Always struggled with these "resolutions" to the twin paradox. The scenario I put together is what happens if a traveler flies past an observer near the speed of light before decelerating and stopping (relative to the observer), I'm assuming that at the point they pass each other they both will see each others clocks running slower. Then some time later the observer accelerates slowly and catches up to the traveler, but stays at speeds much lower than the speed of light. If there is a difference in their ages then it must be due to the 1st change in velocity since the second change can be arbitrarily small and presumably avoid relativistic effects. If that's the case how do you know whether the traveler decelerated or the observer accelerated? Your scenario seems to indicate a link between this and Mach's Principle; which is another area I've always struggled with. If I understand correctly both seem to imply that there are some reference frames that are more inertial than others and that they are linked to the "global" presentation of the universe i.e. background stars, galaxies etc.

2:30 The perspectives aren't equally valid. Whoever fires the rockets on their spaceship can feel themselves being accelerated, i.e. pushed into their seat cushions. 6:40 Same thing: Except for gravity, you can feel acceleration. 7:00 I think you're overinterpreting GR. Free-falling frames are equivalent in GR, regardless of the gravitational field. But that doesn't include frames of objects that are accelerated by other forces. 7:15 The frame on Earth's surface isn't free-falling, so it's not "valid". 7:30 There's the vacuum. At least one of the objects is moving relative to the vacuum. 7:40 A scale with a 1kg object on it will tell you how much you're accelerating. 8:20. The stars are no more important than Earth. What's important is the spaceship's immediate surroundings, i.e. the vacuum. That's the only thing that can directly affect it. I like your references to Emmy Noether, but what about Lorentz? He has the answers you're looking for. Time dilation is caused by absolute motion through the vacuum, which DOES have a reference frame, even though we haven't detected it yet.

Accelerate is absolute because you can measure it in your reference frame.

I wish _everyone_ would stop talking about return trips. Return trips are not necessary to manifest and then observe time dilation.

When the solutions say that the twin in the spaceship accelerates, then they are talking about Proper acceleration. Proper acceleration is absolute. It does not depend on the frame of reference.

Thank you for this video. I watched many twin paradox explanation videos and always had the same issue. All of them instantly assume that the earth twin is fixed in space and only the space twin is moving and they cited acceleration as the source, paradox solved, video ended. But I always thought: but what about the perspective of the space twin??? If he thinks he is stationary in space, he will see the whole earth accelerate and come back. Why does no one ever draw spacetime diagrams where the space twin is stationary and the earth does the V-shaped motion and somehow show me that it will get another solution than for stationary Earth spacetime diagrams? The hint here that the fixed earth and stars in the background give some context to who is "more stationary" than the other makes sense and differentiates the two twins now much better. Thanks again.