Solutions to the Twin Paradox are STILL Wrong 

You misunderstood relativity, SR relies on: 1. all *INERTIAL* frames of reference are equally valid 2. speed of light is constant Einstein never claimed that the same laws apply for an accelerating body. But I can see the confusion; intuitively, why you can say that acceleration is absolute is because for example, if you take a mass and give it speed it'll keep that same speed when you stop acting on it. if you accelerate a mass and stop acting on it it'll stop accelerating according to the lab. in the video you can't switch to the other diagram because it's accelerating. I don't understand if you think that physics states that acceleration is not absolute, or you're aware that you made it up

When you talk about paradoxes in relativity, you should use relativity. And in relativity there are so called inertial frames. Lorentz transformation give you the possibility to transform coordinates between inertial frames. If you just drop "inertial", you are not working in relativity! And that's where all your confusion comes from.

When you accelerate in a car or plane away from a location and you accelerate back toward the original location at the turnaround point and finally deaccelerate at the end of the trip, in each case, you feel a constant pressure against your chest. Conversely, the person on the ground waiting for you to make the journey feels none of these 3 cases. That is the difference and can be directly measured and experienced. That constant pressure demonstrates you are curving your worldline into the space dimension in the direction of travel and back again to the original direction. You can try to work around this by having the car on an aircraft carrier and the aircraft carrier accelerating in the opposite direction in exact sync with the car to keep the car stationary. If you ran this experiment, the person in the car besides at the gear change points, would feel no constant pressure against their chest. You could create a similar situation but make it so the motion of the aircraft carrier relative to the whole is not observable, but in that case, what is relative is the immediate change of velocity relative to your immediate past self. This is different from other forms of velocity and acceleration. In fact, right now sitting or laying there, you are rotating with the Earth at 1,000 miles per hour, around the sun 18.5 miles per second, around the galaxy 140 miles per second, toward the great attractor 370 miles per second but you feel none of it. You feel stationary in space and are moving only in time. That actually hints at the answer and where the weirdness comes from. We only move in time, not space. If we did, our thoughts would be able to separate from our minds but that doesn't happen. Special relativity happens when you accelerate in a direction in 4D space and that direction becomes part of your timeline (aka worldline.) But the size of the observer doesn't change, so as your experience incorporates a dimension in space as your timeline it necessarily extends your timeline out when observed from your previous self trajectory through 4D space. However, the experience inside the "rectangle" is always a "square" and instead if you could look at your past self you would see the same relative changes - shrinkage in the direction of travel and elongation of time (i.e. slowing of the clock for those who didn't accelerate but were in your same frame of reference.) A second part of we only move in time is that though we experience time as a fluid thing, space is static. The subjective experience of time is defined as a spot in space with low entropy in the beginning and higher entropy at the end. Because it is experienced, effectively that section of space is "played" to create the subjective experience such that we cannot observe this section of space. This is what makes time and space complex to one another (as math is a description, not an explanation and the use of complex numbers allows us to describe how subjective experience hides our path through 4D space which we experience as time.) This is not a new idea and dates back to Zeno's arrow with the Greeks or the concept of Maya in Hindu texts. Finally, you can replace the aircraft carrier accelerating with a gravity well and use that, as what is happening with geosynchronous orbit, where the astronauts are in free fall but end up orbiting. Again, the feeling of free fall is consistent with the space curvature, combating the curved orbit, resulting in a constant state of free fall. What is interesting in every example is how acceleration is felt. Acceleration, changing velocity in time, is felt in each case as a velocity, a constant pressure resisting your acceleration. This hints at the fact we are really a velocity in spacetime, traveling in time. If not we should feel an ever-increasing pressure against our chest when accelerating relative to our past self. If you walk thought the math from this perspective, it does add up. We move only in time which means acceleration causes us to change space travel into our timeline as at a constant velocity we always feel at rest. And since we move in time but space is static, the use of "i" is needed to compensate for our experience as "I" There is a lot more to this though as it also points to subjective experience relating to the structure of 4D space, rather than being substance based, a philosophy we inherited from the Greeks.

Unfortunately this is fundamentally flawed and therefore wrong. The twin paradox only exists if there is no violation of the equivalence principle. Or in other words there's no difference in saying person A is still and B is traveling at a constant speed or person B is still and A is traveling at a constant speed. If that's the case, then equivalence principle holds and there is a paradox. Unfortunately the creator of the video made a fundamental mistake in thinking the equivalence principle could apply to acceleration. Unfortunately it's just not true. Think of it this way. Imagine A and B are both in separate rocket ships, but only B fires rockets to accelerate. Now imagine these astronauts are hovering just above the self destruct button. Only one of them is going to blow up and it's the one who rams into the button. Since A didn't fire rockets and the ship and the astronaut are moving at the same speed, that'll never happen. Conversely, since B fired rockets, the ship accelerates but the astronaut does not initially because he's not in contact with anything until he hits the button and blows up the ship. To say that both accelerate makes no sense because there would have to be some "magic" force to cause astronaut A to hit his button and there just isn't one.

One factor which seems to be not explained here is that there IS a NON RELATIVE difference between the twins. The twin who ventues forth in the spaceship feels inertial forces that the stay at home twin does not experience. Imagine we had a science fiction "ultra wave" radio whereby the twins could comminicate instantaneouly. The traveller blasts off and phones in saying "man this rocket is powerful! I'm feeling huge inertial force from my acceleration, I'll try not to black out okay?'" In my rocket ship frame of reference of course I'm seeing you and the earth accelerating away from me at the same huge rate. How are you handling the G forces are you well zipped into your G suit?." The stay at home replies "what G forces, the only G force I feel is gravity keeping me in my armchair." Ergo ... the two twins are NOT symmetrical with regards to acceleration forces. You can dicriminitate who is the traveller and who is the observer by comparing their experiences of acceleration. Have a think about it.

Acceleration CAN NOT be relative. This would break the conservation of linear momentum law. Every action has equal and opposite reaction. Relative acceleration would break that. This paradox only proves that physics wouldn't work without conservation of linear momentum.

It's incorrect. Acceleration is in fact absolute.. it's equivalent to gravity, meaning that, just like the metric tensor, it's local.

It's about perception: the MOTION Is perceivable (instead of variable); the DISTANCE and ACCELERATION Are symmetricaly perceivable! But WHAT about the FORCE?? The rocket-twin Is PERCEIVING the FORCE (of propulsion), while the Earth-twin DOESN'T! THIS maybe breaks the SIMMETRY

It's true that special relativity and the twin paradox are hard to explain well, and I appreciate that, but this video is so fundamentally wrong I feel like I'm being trolled. The big error is what when the two symmetrical spacetime diagrams are shown for the Earth and space twin, the Earth twin's spacetime diagram is not showing a single inertial frame. It's showing two inertial frames, one for the space twin's outbound journey, and one for the space twin's inbound journey, and it's mixing these together into a single spacetime diagram as if they were a single inertial frame. You can't do that. That's not a spacetime diagram. It's nonsense. It's a misunderstanding of what a spacetime diagram represents. At 8:45 in the video, the The Earth twin spacetime diagram on the left side of the symmetry diagram is hot garbage. I recommend reading about the version of the twin paradox that has 3 twins and involves no acceleration at all. It's a much more satisfying explanation, and does a lot to address the confusion around acceleration that this video gets caught up on.

One frame is inertial and the other is not, which means one of the twin is not interacting with anything (neglecting the influence of the Earth as the paradox arises in special relativity) whereas the other one is interacting with it's ship. Special relativity is valid only in inertial frames of reference. It is not about agreeing on who's accelerating or not, it's about understanding the specificity of Galilean frames of reference. The traveller experiment forces acting on him, the other twin not, therefore one is accelerating and the other is not, which solves the paradox. The reason why you got it all wrong (and why all the others are indeed correct) is that you believe acceleration to be the derivative of velocity, which is true in Euclidean geometry but not in Minkowski space-time. Acceleration is the derivative of velocity only in inertial frames of reference. It is an observer independent quantity (it's not the case by the power of a genius sense of physics, it's the case by definition of 4-acceleration in special relativity).

Acceleration of frames is relative and only mathematical, but objects move from one inertial frame to another inertial frame of different velocity require force and this is absolute. When the twins start at the same place with zero relative velocity, they can both move away from each other and turn around, and then meet up somewhere not necessarily at the same point. They can compare with each other's acceleration and deduce who is older. The difference in the amount of acceleration is still the key to resolve the paradox. Right?

Clearly the narrator has no clue what he's talking about. Acceleration is the only solution to the problem. And acceleration is definitely NOT relative. Quite the opposite, whereas velocity is (mostly) relative, acceleration is not. It's actually quite simple as you understand it (which the narrator obviously doesn't).

9:16 You’re ignoring the fact that Albert’s coordinate clocks (imagine them distributed through space and riding with him) would no longer be synchronized in his new frame after he turned around. This seems like an easy way to distinguish instrumentally who changed their inertial reference frame and coordinate system. Alice’s clocks would always be synchronized so her calculation is more correct. With Albert he’d have to decide how to resynchronize his clocks which is basically cheating. If you change your clocks mid race, you don’t get to declare yourself the winner.

No acceleration is not coordinative. Proper acceleration is a scalar all observers agree on.

I haven't seen the follow-up to this video yet, but the confusion about the "relativity of acceleration" appears only if you constrain yourself to the kinematic definition of acceleration, which doesn't distinguish between acceleration due to real forces (e.g. rocket propulsion) and pseudo-forces (such as Coriolis forces). One can use this measurable distinction to justify which of the two travelers changes the frame of reference. That's also true for the discontinuous jump approach in 11:01.

I don't see how you can claim acceleration to be relative, when it exerts a fictitious force on the observer. So how can the twin at an inertial rest frame claim they are accelerating when they feel no force? I would really appreciate an answer to this question, because without it I simply cannot accept your assertion as it simply makes no sense to me.

Acceleration is in fact absolute. And it's easily testable as well: With a weight attached to a spring. If you are in an inertial frame of reference, the spring will not move. If it does move, you are accalerating and thus not in an inertial frame of reference. You can't draw two space time diagrams that are valid for each twin, because one has to accalerate, which again, is easily provable with a spring.

You are wrong. Sabine Hossenfelder just uploaded a video entitled "Special Relativity: This Is Why You Misunderstand It." It should help you to find out how you were mistaken in thinking the acceleration is symmetric.

The resolution of the twin paradox is very simple. In Minkowski geometry the "length" of an everywhere time-like curve is interpreted as the proper time along that curve. Clearly Emmy and Albert travel along different curves. The fact that their length (ie. proper time) is different is no more paradoxical than the fact that the hypotenuse of a triangle is shorter than the sum of the catheti. When you put it in the proper geometrical framework it seems absurd to call it a paradox. Indeed, the paradox only arises when we insist on teaching relativity using Einsteins original approach (rather than the modern understanding that has developed in the 100+ years since) of confusing "gedanken" experiments and postulates. In particular, misapplying the principle of relativity, i.e. insisting that all motion is relative and both accounts are equally valid. They're not! The journey from Alberts perspective simply cannot be explained in one single IRF. So the diagram at 4:40 is highly misleading, whatever coordinates you're using to draw that diagram are not inertial and so does not have the simple interpretation of a normal space-time diagram. The insistance that acceleration is relative is the problem here. Four-acceleration of worldline is defined as the covariant derivative of 4-velocity along the worldline. This is a completely coordinate invariant definition, and all observers will agree on the norm a^2 of the acceleration. For one of them (Emmy) this will be zero the entire trip. For the other (Albert), it will not be. They don't need to "agree" with each other to establish this.

Acceleration is absolute. This is an important point in the theory of relativity. To measure acceleration, you don't need a reference point. So I still have to wait for a video that helps me understand.

Here is the correct solution to the twin paradox. One twin is on earth and the other leaves the earth to mars and then returns. So the traveling twin has been in TWO DIFFERENT INERTIAL frames while the stay at home twin has remained in a single inertial frame. YOU can not assert symmetry ! Now I have heard Einstein mentioned the idea of GR to solve the twin paradox. The idea is in GR given paths between two events the geodesic path is the path of longest proper time. The stay at home twin is following the geodesic and hence will have the longest proper time. In flat space time both the GR and SR give the same result. The stay at home twin ages more.

So, you are almost there... In the same way that Maxwell had to fudge his equations because he was dealing with the flow of charge when he should have been dealing with fields, you are still struggling with concepts like acceleration and time. The key is that light doesn’t experience this universe - either in terms of time or space...

Forget the Earth. Place Alice and Bob in spacetime with no other masses. They separate from each other at a certain rate, say, .9c. At some agreed amount of time (each of their clocks), they come back together. Their biological ages are identical.

The twin paradox consists in comparing two paths in spacetime that form a closed loop. One of them has to be shorter. The observer on the ground is in free fall through the Universe whereas the observer on the rocket is not. Free fall trajectories have the longest proper time (they're maximizing geodesics) so the guy that stays on earth is older. This can be measured experimentally. The notion of being in free fall in the Universe replaces the notion of aether from the XIX Century as Einstein proposed. He wasn't against the ether and argued for it in GR. It was just of a different nature than he had encountered in his youth.

01:57 _Twin B has the same right to say that twin A is accelerating towards him._ As long as you leave out any idea of gravity, I don't get this. If you accelerate, you not only measure this but outright feel it, you feel a force that seems to accelerate you towards the rear wall of your cabin. O.k., A feels weight as well, since he's pulled to Earth by gravity but if we replace Earth with an inertial space ship gloating in free space, twin A will feel weightless. The only way to justify your assertion above is that A is that A is passively accelerated by some homogeneous gravitational field which B resists. In this case, A comes from a higher gravitational potential.

You seem to be of this mindset that we cant measure and compare 2 different accelerations because for some reason we can'tfell forces. But like, how does that explain the fact Nasa or whoever would have to use a certain grade of steel with a particular yield strength for the rocket ship for instance, so the stiffness of each member would have to be designed so that it can withstand the forces resulting from the acceleration it is subject to? Like we measure forces resulting from accelerations all the time from the stress vs strain relationships of materials such as steel.

Dialect, you need to understand the differences between a constant speed, velocity, and acceleration. A constant speed is a scalar quantity denoting just how fast (distance per unit time) an object moves as seen by an observer. Velocity is a vector quantity meaning the direction counts. Acceleration is ANY change in speed, direction, or both. Even if ONLY direction changes and not the scalar speed, there is an acceleration. An observer in space that is not accelerating and not in any gravitational field cannot know if he is stationary or moving. It is all relative. That is an Inertial Reference Frame (IRF). If one is in the void of space in an IRF and observes movement relative to another IRF, either IRF could decide to choose who is stationary or who is moving. Both would be correct as that is Special Relativity. Failure to see that both could make the same judgment and insisting that the velocity of light is still ‘c’ when one IRF observes another, led Einstein to his famous thought experiment generating the error about time dilation. The meaningless twin paradox is just going further down this wrong rabbit hole.

There is too much unnecessary confusion about this paradox. Emmy and Albert don't have to agree to anything but all inertial observers in the universe would agree on who was the one accelerating and this is what breaks the symmetry of the twin paradox.

Remark 1: There is no "Twins paradox". It's not a paradox. It's a real, physical effect. The twin who goes away ages less. This is a clear and simple prediction of the Theory, which is experimentally confirmed by the synchrotron muon experiments. As for resolving the riddle why the twin who goes away (incorrectly) considers it is his brother whose time was the more dilated, it is a non-question. This is Special Relativity. Observers in the Theory are Lorentz observers. The twin who goes away is simply not one of them. His considerations are thus inadmissible in the Theory. All that matters is all Lorentz observers agree.

You keep asserting that the motion is perfectly symmetrical and can be flipped around and looked at in two (actually infinite) different frames to all come to contradictory conclusions. This is simply not true in SR in a flat local Minkowski space. You are simply eliding over what inertial movement actually is, how inertial frames are defined, and what inertial movement actually means in SR. You are essentially asserting that an inertial frame can be attached to any / every observer, regardless of any forces / acceleration, and no one can distinguish between them if they only have one another to measure against. That's not true even in Newtonian / Galilean physics. Accelerating observers will perceive forces that seem to be affecting everything, including themselves. For example, a Merry-Go-Round rider will perceive almost the entire universe spinning around themselves (or the central axis of the ride). They will also perceive a fictitious force that is seemingly trying to throw them off the ride in an outwards direction. What is actually happening though is that the Merry-Go-Round is spinning (not the universe) and it is constantly PULLING the rider INWARDS towards the center altering their straight line, tangental, inertial motion that Newton's 1st law says they would otherwise follow (e.g. - if they stop trying to hold on). Going back to your favored example of two twins moving relatively apart and then coming back together, we can experimentally set that up and completely blind the participants by putting them in black boxes floating freely in space. In SR in a flat local Minkowski space (i.e. - no gravity), no matter how you do it, at least one of the twins must experience forces that cause the twins to separate and then come back together (e.g. - their box will run into them and then push against them). Depending on the particulars of who is actually experiencing forces (e.g. - firing their rockets or not) and how much, that will determine which twin's clock will have run slower (or not) in SR when they both come back into the same frame and compare ages. If we actually did the experiment I laid out above and my box remains in free fall (i.e. - it never touches me nor pushes against me) while the other box experiences 1000 g's of force for a significant period of time, then it will be obvious to all by the blood splatter in the other box which twin accelerated and which remained in an inertial frame. That's why I REALLY don't understand why you think acceleration and forces are entirely symmetrical, solely coordinative, and can't be felt. The bloody pulp of my unfortunate twin begs to differ. Now, I've put a lot of emphasis on acceleration in the above because it is an absolute thing that can be measured (i.e. - forces that are acting on you can be measured with accelerometers), which you seem to dismiss, ignore, or disbelieve. But the Twin Paradox is really more about INERTIAL frames of reference, relative velocities, and ultimately in what frame you measure or care about. In SR in a local flat Minkowski space inertial frame of reference, all inertial movement will be in a straight line: the world lines of all inertial observers will ALL be straight lines in EVERY inertial frame. A clock in the "stationary" inertial frame that we care about and ultimately compare ages in will run faster than clocks in every other inertial frame that is moving relatively to it. If / when an inertially moving clock boosts into the frame about which we care (meaning its world line will no longer be a straight line but be curved or kinked), then we can directly compare clocks and it will have run slower than the stationary clock. If the inertially moving clock never boosts into the frame about which we care, then the relative motion DOES remain entirely symmetrical and reversible, the observers will disagree on who is aging more / less forever, and we can't assert that either is correct or incorrect. Only once they both come into one agreed upon frame in which we compare can a direct comparison be meaningfully made. Or, more generally, we can only say whose clock has run faster or slower in any one particular frame we all agree to use to measure both of their passages of time in that frame.

Acceleration IS the answer. The one who is accelerating is feeling it, the one who is not - is not, so the symmetry is really broken. In relativity acceleration can be understood as a failure to move geodesically with respect to the local intertial frame. This is especially important in GR where acceleration "towards" over long distances is undefined, because there is no unique way to transport vectors belonging to different tangent spaces. On top of that, the real time experienced by either person is the proper time, and the coordinate time does not always match the proper time. For given two points in spacetime it is the shortest for non-accelerating person, because the faster you move through space, the slower you go through time. Finally, forcing the non-accelerating person to move on a curved line with the accelerated one following a straight line requires a certain coordinate transformation which also changes the metric tensor. In these coordinates metric tensor assigns lengths in a strange way, giving more proper time to some straight lines and giving less to some curved ones. All of this can be rigorously checked using geodesic equations with and without 4-acceleration and the integral definition of proper time. So, whenever you discuss fancy coordinate systems and start drawing straight lines, please show the metric tensor which you use to assign distances.

Acceleration is not relative. If both twins have a pendulum bob hanging from their finger, the one on Earth will see that it remains still during the turnaround, indication she is in an inertial frame. The twin on the rocket will see the bob move forwards during deceleration and to the read during acceleration. Thus both twins know that it is the rocket that accelerated. That is why Einstein's first postulate mentions Inertial Reference Frames.

The two are not symmetrical. Once the traveling twin deaccelerates, they are no longer a conventional reference frame. The astronaut pilot will feel an inertial force towards the dashboard and the carefully constructed house of cards in the break-room will topple. From the point of view of the space ship, the Earth may *appear* to slow its acceleration, and then *appear* to rush back towards the ship as the traveling twin turns around, but when spying from afar their Earthbound twin's environment, nary a jiggle of Jenga tower on the kitchen table will be seen. These inertial forces are how the two can divvy out who is the one actually doing the "turning around".

Acceleration is not relative. You can't simply pretend you're being accelerated because you can see someone else strapped to a rocket. Once you get that wrong, all your subsequent conclusions are wrong.

8:51 While BOTH accelerated from each other's point-of-view, it was only Albert who ACTUALLY accelerated from the starting point, necessitating huge amount of force to divert from the earth trajectory while the lady simply STAY with whatever existing trajectory she was in. If I were with a friend, asked him to stay in place while I run a kilometer away and back to him, we BOTH accelerated from each other's perspective, but I can surely tell who lose a bit of body weight.

How is acceleration relative? If so, then when I shine a beam of light from my torch, is the light travelling at light speed or am I? Obviously it's not me.

There is one solution that can explain the twin paradox, but it is not even up for consideration. This is heresy, but I'm going to say it: RELATIVITY IS WRONG The problem with relativity is that the equations themselves are sound, but the name relativity has been taken too literally. When you examine the equations of relativity, there is not a single one that refers to the objects relative to each other. Rather, everything is relative to or the speed of causality. The time flow for each twin is not relative to each other, it is relative to the fraction at which each moves in relation to

Acceleration is absolute.

The real key to show there is no paradox is Rlativity of Simultaneity.

This relative nature of time was first introduced in terms of moving clocks and photons. A clock moving away from us will seem to tick slower to us due to increasing distance each photon has to travel. Now, let us think in terms of photons and clocks for this paradox. What’s stopping us to say they both will be same age when he comes back? When Albert goes away, his photons reach us slowly due to the increasing distance making him age slower to us. Same can be said in Emmy’s frame of reference. When Albert comes back, his photons are received in fast succession, due to decreasing distance, countering his slow aging from moving away, making him the same age as Emmy. Same can be said from Emmy’s perspective.

Why not have both twins in spaceships ... they go apart ... both turn around and return to each other ... logic says they will be the same age, but doesn’t that violate both perspectives that the other’s clock was running slower or does the turn around somehow (simultaneaity...) get them in sync at the end?

It's relative to the reference frame. The planet would be moving in reference to the star it's orbiting, the rocket is accelerating vs the same reference frame. One is moving faster relative to the other. This would cause the time dilation between the planet and the rocket. Your mirror calculation misses the fact that even from the earth's perspective earth is not accelerating vs the rocket. Earth is in orbit around a star. The only acceleration earth experiences from the Suns reference frame is tiny vs the rocket leaving orbit and returning. Earth clearly isn't accelerating nor could their clock not be ahead of the rockets. Things in orbit of the planet have clocks that go out of sync. If earth was accelerating then it would leave it's orbit around the sun. If the entire solar system was accelerating, it wouldn't change the fact that the rocket is moving faster relative to the sun, than earth is to the sun. The solar systems movement or the galaxy's movement doesn't change the reference frame to the sun. Nor does it matter since we are in this reference frame. Even in deep space your reference point would be the great attractor. Using the frame of reference of the other person in deep space is not using the formula correctly.

@dialect What’s your response to the top comment which argues that the accelerating ship can be distinguished by dropping apples in each?

I don't know if anyone will see this, but isn't acceleration the same as gravity, and that has a different time dialation effect because it stretches spacetime? So in the case of the stationary twin paradox, one twin does not experience traveling through a stretched spacetime whereas one twin does. And so his time dialation is supercharged, essentially like the black hole section in interstellar. So dialation due to velocity applies to both, but dialation due to acceleration happens only to one, and only one twin expends energy to do so.

The twin paradox is not so much a paradox as it is a misrepresentation of time dilation physics. Without an acceleration component there is no time dilation. The point that the earth twin's perspective being just as valid as the rocket twin's perspective is irrelevant--a non sequitur. What is relevant is who, in fact, is undergoing acceleration. That's it! It's not a matter of what the twins agree on about who is moving. It's not relative.

This is so very wrong. I was subscribed but there are too many nonsense videos

Thank you for your work! Is the lack of symmetry related to the fact that the earth would need more energy to accelerate? Or that it's change in momentum would be less?

Sorry for my ignorance, but when you tell that one twin will be older than the other, does traveling fast also affects particles decay? Will one twin Literally have grey hair and wrinkled skin and the other one look like a teen? Or will they just feel that X amount of time had transcurren differently and physically look the same?

Sees to me that accelaration is distinguishable. The one in the spaceship has to turn off the engine, then use thrusters to turn around and then fire the engine again to accelerate back. The person on earth doesn't have to do anything and yet it is changing in direction of motion?

Thank you very much for discussing this topic. It is a shame that these videos you discuss enjoy hundreds of thousands or some even million of views, while this one has less then 20k. Having said that, I think that you are risking of confusing or misleading your viewers by saying "acceleration is also relative" without any caveats. When you check the banking accounts of Albert and Emmy you will notice, who paid for the fuel. Acceleration is relative only in kinematic description. Your statement between 2:51 and 2:59 is false.

Which formula is used in 11:06?

A version of the twin paradox without accelerations The classic twin paradox is "explained" because there is acceleration, but in this version of the twin paradox there is no acceleration and I do not see how the dilation of time could be explained. Bob is standing on Earth and Alice is on a distant planet at a constant distance from Earth. Their watches are already synchronized in the following sense: Suppose Alice's planet is a light-year away from Earth. Bob emits a light signal to Alice at time t = 0 according to Bob's watch. When Alice catches the signal, she sets her watch to position t = 0. Bob sets his watch to t = 0 one year after the signal is sent. Now Bob and Alice's watches are synchronized. Alex stands behind Bob, then accelerates and the moment he overtakes Bob his speed stabilizes. At that moment they are synchronizing their watches, and this marks the beginning of the experiment. It does not matter what Alex did before the clocks were synchronized, so his acceleration does not count in the experiment. Alex continues his journey until he gets too close to Alice. At that moment, Alex photographs his watch and Alice's watch at the same time, and immediately after that, he slows down and stops. If at that moment Alex compares his watch with Alice's watch, he should not find a significant difference from the difference between the photographed watches. Because Alice and Bob's watches are synchronized, it is not necessary for Alex to return to Earth to compare his watch with Bob's watch. In this experiment we can assume that Alex is motionless while Bob and Alice are on the move. However, both alternative reporting systems are different aspects of the same events. This means that the photographed watches will have the same difference in both reference systems. But these reference systems are equivalent, as there is no acceleration. Without acceleration we cannot justify the dilation of time for any observer of the experiment. So I conclude the photographed watches should not be different, ie they do not record any dilation of time. The question is Comparing the photographed watches, did Alex's watch gain or lose time compared to Alice's watch?

paraphrasing sabine, with regard's to newton's bucket: acceleration is NOT just a change in speed. for the water to spin around in the bucket it has to change direction, i.e. accelerate. it was not a paradox to begin with.

I'm very sorry, my friend, but this is objectively wrong. Twin B does NOT have the right to say that others are accelerating while he remains still. That is 100% false.

It seems to me that although each twin sees the other recede and then approach in the same way, this doesn't imply that either one could be doing the accelerating. Saying, "the paradox disappears if the twins agree on who is doing the accelerating' doesn't mean there are two (or more) equally valid answers. It means that one answer is true and the others are false. The twins agree because one of them, and not the other, IS accelerating, which implies that there wasn't a paradox to begin with. As an aside, the apparent paradox that everyone sees everyone else's clocks going slower, but never faster, is analagous to the fact that we always appear smaller, but never larger, as we move further away from someone. What's more, two people will always see the other as getting smaller by the same amount. Obviously. Similarly, no-ones clock really 'slows down', just as people don't really shrink as they move further away. The analogy can be extended to velocity and acceleration, but I'm kinda tired now.

So, may be a little of a stupid question: but if while moving away from the earth, your seems 1.06 times slower, "turning around" (i.e. changing the velocity direction, no matter the reference frame) won't time appear 1.06 times faster? Because the sign changes in Lorentz equations? So basically they cancel out, and no one is older? Can someone help me with this?

I'm puzzled why this narrator thinks acceleration is relative. Acceleration IS felt and that IS a critical concept. In the normal universe, the traveler will feel when they are experiencing acceleration, and thus will feel it when their direction reverses. In no frame whatsoever will the rest of the universe feel the acceleration that the traveler does. And he says 'you have to remember "firing rockets" or "turning ships around" does not constitute acceleration. Acceleration is purely coordinative.' No, acceleration is not merely math or graphing, it's a very real physical phenomenon. Now, whether acceleration is relevant to the twin paradox, I'm not sure, I'm just saying this video is badly wrong. I'm afraid the ultimate problem regarding whether acceleration is part of the paradox is that the Twin Paradox is just not worded precisely enough to stand up to the kind of debates surrounding it.

Please make another Video. I think your resining is festinating. I would love to hear your take on the solution of the paradox.

The slide at 10:22 shows that the frames behave _not_ symmetrically. Are you sure you can set t_B=t'_A in 9:39?

Acceleration can easily be eliminated by a simplified thought experiment. Since time dilation supposedly accrues continuously and uniformly throughout the journey, the two twins simply send a radio message stating how much time has passed and neither twin changes direction or accelerates in any way. After a time lag, each will receive the other's report. Will they report the same amount of time has passed because there was no acceleration event to "lock in" the time duration difference?

This video is not good science. You misunderstand an important premise, then use that mistaken premise to discredit these other videos. Acceleration may be mathematically relative in Minkowsky space. But physically, acceleration is experienced differently than velocity. This is the broken symmetry you don't understand. If Al is standing in the middle of an ice skating rink, and Betty is traveling away from Al towards a wall, the acceleration that Betty experiences by pushing off the wall is not symmetrical. Imagine she accelerates so fast she breaks her arm. By switching to Betty's reference frame, Al doesn't magically accelerate fast enough to break his arm. Your conflation of velocity with acceleration is a high school physics level error.

The twin "paradox" can easily be solved without mentioning any acceleration! You only need to know how clock synchronization works and realize that inertial frames of reference can't "turn around". Detailed calculation shows, and it can even be visualized with a space-time diagram, that there's no paradox at all. BTW acceleration is not relative. If it were, the Equivalence Principle would be false and General Relativity would be incorrect.

If we are all happy that velocity is relative I don't see why acceleration is different. Your spring device being used to measure this acceleration is useless unless you set it up relative to the direction of your velocity. And just because you feel that acceleration, once again, you feel it in the direction relative to your point of origin. It seems pretty relative to me.

If you put a clock in a gravitational field it slows down (watch the movie "Interstellar"). This is because a gravitational field is an *acceleration* (e.g. 9.8 m/(sec^2) on Earth). It takes an acceleration to slow down a clock (and NOT velocity alone). The twin that moves must accelerate. Only *his* clock slows down because of this acceleration.

Well don’t you have a problem at 5:32 in the video? You can’t draw the diagram on the left because Albert accelerates and therefore he needs 2 different space time diagrams to describe his motion. Albert knows he accelerates because he can feel it and since he can tell that Emmy accelerates at the same rate he measured himself accelerate at then it must’ve been him and not Emmy that has accelerated. In this case Albert has to draw 2 space time diagrams.

I also have to disagree acceleration is not releative. it is something that can be felt. constant velocity is relative. but acceleration is not. For instance twin B accelerating to the speed of light (which is necessary for it to experience time dilation) he will experience a force on his body. As acceleration results in a force. Twin A will not experience this force on their body as they are not accelerating. So both twin A and B can agree that it is B who is accelerating and not A. For the twins to seperate and then meet each other again, there has to be acceleration and deceleration change in direction and acceleration and deceleration etc. all this change in speed and direction is called acceleration in physics. So one twin will experience a force the other won't. And it is this twin who is the one experience time dilation. If for some reason you argue that tein b never experiences acceleration or deceleration and just travels at the speed of light. then the question of which twin is younger is never answered as they never meet. so both twins will say theoretically the other is younger but the question can never be answered as they will never meet. so in effect a schrodingers twin will take place. it is only when they both meet does the question get resolved. much like schrodingers cat, the question can only be answered when and if they meet.

This entire video is wrong. Acceleration IS the answer, and here's why: While velocity is relative, in SR, acceleration is ABSOLUTE. That means, in any reference frame, you can determine whether or not your frame is inertial WITHOUT REFERRING TO OTHER REFERENCE FRAMES. How? You simply build an accelerometer, or do something even simpler like letting go of an apple you're holding and seeing if it moves. Setting aside gravity (we're assuming a flat Minkowski spacetime), the apple you let go should not move if you let it go. If it does, then you are in a non-inertial frame. In other words, if there exist fictitious forces in your frame, then your frame is accelerating and thus non-inertial. If, after conducting this experiment, you see that you are in a non-inertial frame, then you must use *DIFFERENT* equations in SR to account for this fact. If you do, then you will get the correct answer. So in our example, the twin on the Earth (again, IGNORING GRAVITY), will detect that they are in an inertial frame. The spaceship twin WILL detect that they are accelerating, so if he adjusts for this by using the correct equations of SR to account for this, then when he wraps back around to Earth, his math will match the Earth twin's math. I'm shocked and disappointed. I thought that this channel was good, but now I'm unsubscribing since it confidently posts FALSE information as if it were true.

All videos and explanations I found on internet are dumb and miss the point. Why no one can provide a clear explanation of a phenomenon that was already proven right for a century now? This is the biggest puzzle for me.

Acceleration is not relative.

So are gonna have to wait another year for another video on this from you?

There is a fundamental flaw in your calculations under coordinates for the turnaround and that is that you are ignoring what each of the twins is actually experiencing. The twin that stays on Earth sees the trip as covering 1LY and thereby experiencing 2 years. The other twin sees a trip as covering only the √3/2 LY and experiences only √3 years. So when you look at what each one actually experiences the Paradox goes away.

You seem to be leaving out one thing: if you consider the ship "stationary" and the earth to accelerate, the ship twin's space time diagram will NOT be a mirror image: it will still be shorter for the ship than earth, because the total distance "traveled by earth" in your example would be 2 ly while the total distance traveled by the ship would be 1.73 ly. You can't ignore lorentz contraction of the distance in the ship's frame, it's an integral part of SR. Whether you consider proper acceleration or not, it's not symmetrical. Those other explanations aren't saying you must consider the ship's proper acceleration, they're just explaining what happens if you do.

I’m so glad I’m not the only one who watched most of these other videos and said “wait, what??…..that doesn’t answer the question.”

The video criticizes others explanations but never offers one.

Hey. Great video. Assuming relativity is actually how I've pictured it, I would agree that the paradox can't be solved using anything we could mirror conceptually from one observer to the other. One thing to note though: How did you lose the symmetry in your math? If the motion (speed, acceleration) is mirrored shouldn't both perspectives be perfectly mirrored as well? IE: They both agreed for your final step in the diagram (3.46), but your intermediates results didn't seem symmetrical. I'm not sure if it's the negative speed (something can't move slower than stopped but my instinct here is to say moving closer or farther is the only true way I can describe my motion relatively without an external reference frame (the concept of crossing the axis in cartesian co-ordinates basically is a reference frame "feature")). I am unfamiliar with the correct way to use the Lorrentz Transformations though.

9:32 Are you saying that direction matters? How do Albert and Emmy determine the other's direction? Relative to what? Please explain this in more detail.

There is indeed a lot of confusion surrounding this issue, and it seems that you guys are adding to it. A body in free fall is experiencing no net force, whereas an accelerating body does experience a force. For that matter, the twin that is accelerating could be in a locked room with zero knowledge of goings on in the external world, and would still have to experience a net force. Thus acceleration is not relative, and both twins would have to agree on who is accelerating, and that's the solution. It's also, I duly note, the solution offered by the better science youtubers, like Don Lincoln of the Fermilab RU-vid channel. Also, no one is missing any time, but is instead measuring time along different paths. Likewise, if two parties decide to travel by car to a certain destination, but one goes by the scenic route, while the other takes the direct, at the end of their journey, while one has traveled a longer distance, the other is not in any sense 'missing' that distance. That's just a profoundly misleading interpretation of a certain way of doing spacetime diagrams, and goes to show that one must exercise great care when attempting to extract metaphysical meaning from operational procedures. What may add to the confusion is that while in Minkowski spacetime, time is measured along a path, same as distance is when going on a nonrelativistic journey, and with a certain distance, the null distance, being the shortest possible between two locations, in spacetime, the null duration between two events is the longest possible time, thus contradicting our probably innate naive intuition about how distance works. I like your channel, you're doing good work, and I'm still subscribed and all. But this one is, in the words of Postmaster Kevin (aka Agent K), a case of 'go home and do it again'. Or perhaps go home and consider very carefully whether you really need to be doing this relativity stuff at all. Oh, and do give a thought also to whether your confidence is not sometimes somewhat misplaced.

You can't solve the twin paradox by drawing a space-time diagram INCORRECTLY. Imposing rectilinear coordinates on a Minkowski space-time will result in incorrect calculations.

I've watched both videos and those of others. I await your third video where you give the true answer to the paradox! When will that be released?

You left out that the rocket gains mass as it accelerates, as well as time slowing. The earth is NOT accelerating away from the rocket, as it is using no energy to do so, so it shows no mass gain or time distortion The rocket is obviously using such energy. The authors argument is visual only- No other parameters are invoked

It was so funny what you said at the end of the video. The symmetry between the observers was broken when the one of them turned back. The observer on the Earth is in the inertial reference frame. On the other hand, other observer would not be in the inertial frame when he turned back. He would be in the non inertial reference frame. If two observers do experiments at each time interval to demonstrate which one is in the inertial frame, the observer who is not on the Earth clearly understands that he is not in the inertial reference frame. Maybe you can think that you are in the car and your friend is at rest. You go away and then turn back. Talk with your friend. You would not say that you don't accelerate.

If acceleration counts, shouldn't DEceleration also have effect?

Beside the fact that accelaration is not relative, there is the problem that diagrams of non-inertial systems are not that single. If you want to draw a picture of what happened from the perspective of the one who left that is not that simple as to invert the picture. For instance, the constant time sections for that observer that left the earth are not straight lines when he is accelerating. There is a point where a human must accept the limitations of the human mind, stop waving hands and do the necessary computations. In this case, you must recreate a more realistic setup, like smoothing the curves to avoid the infinite acceleration, namely think of a finite acceleration at the beginning, at the middle, and the end, and then compute the proper-times of both observers using line elements of a Minkowski space. Surprise, the twin that left the earth, and returned, expended less time than the one at the earth. Voila, the mystery is over.

I'm tempted to design some animations that address the slow vs fast clock trope that is always used in these videos. Just saying that someone's clock ticks slower doesn't provide any insight into that reference frame, Alice, Bob, space, time...or clocks. A more intuitive analogy would be to treat space like air or gas, time like air pressure and the difference in observations of clocks like an index of refraction between the two pressures. I would refer to it as fast space and slow space to address rest frame and inertial frame. At least this way, if you are saying that someone's clock is ticking slower, it must mean you are observing it from "fast space" perspective, and this highlights the elasticity of time in SR whilst preserving all clock ticks in both frames.....if you get what i mean..

2:00 Ummm no? All you need is a cup of coffee in your hand to tell if you’re accelerating. There are many tests for whether your frame is inertial. Also, if you do Lorentz transformations on the space time diagram, one line is always straight and the other is always kinked. Which does the accelerating is boost invariant Inertial frames being special is like day one high school physics man, and it’s reiterated by Einstein too, so it’s not like they stop being special when relativity comes into the picture. 9:00 You did the transformations for each segment of the world ones separately, not the whole trajectory. You’re only considering the parts without acceleration because you’ve decided acceleration doesn’t matter, but it does. I like other videos of yours, and I agree there’s many flaws with videos about twin paradox out there, but yours has significant flaws too. I’m also not some random idiot who’s watched a few vids and thinks they know it all; my research as a physics PhD candidate involves relativistic plasmas and I have friends I study QFT with, so I had better understand this stuff well.

Your solution is wrong. For the case where one of the twins is in the inertial frame and the other in an accelerated frame (back and forth), special relativity is fully applicable and works well. At minute 1:50 min you say acceleration is relative, yes, but for a third system, it's not relative for the twins. One is in the referential without acceleration and the other feels and experiences an acceleration. There is no symmetry. The twin that goes and slows down and speeds up to come back gets younger. This is a simple calculation in special relativity. General relativity is only applicable if we include gravity.

General Relativity (acceleration) as a "solution" to the TWIN PARADOX reintroduces absolute motion, but not consistently. Q: Which of twins will be old and gray? A: The twin which wasn't moving! He wouldn't experience the time dilation. Q: But I thought each twin could consider the other twin to be moving! A: Nope, if the twins were initially together in an initial inertial frame, and then relative motion occurred between them, one of the twins must have accelerated over some period of time (hey! hey!) to bring himself eventually into a different inertial frame from the other twin. General Relativity then applies. Q: I see, so GR reintroduces absolute motion: The object that has, once upon a time (whose time?), accelerated relative to another object is TRULY MOVING relative to the other object. The younger twin is younger precisely because he was truly moving relative to the old & gray one and we can tell this by the fact that he is young and other is old & gray. Isn't that what you are saying? A: Um... Q: And can't the time period over which is the "moving" object is accelerated be made arbitrarily small, in theory? A: I suppose.. in theory... Q: I must point out the Lorentz transformations do not contain any acceleration terms whatsoever, so if, as SR claims, these easy transformations apply once neither twin is accelerating, i.e., once the two twins are in different INERTIAL frames, then it follows that which side of the equation the factor "(1-v^2/c^2)^1/2" appears on depends upon which object is truly moving and that is determined by HISTORY. Doesn't that follow? A: Umm... Q: Of course, Lorentz & Poincare thought the speed "v" in the transformations was the speed of the object relative to the absolute aether & so none of these paradoxes appeared; it was Einstein who decided that "v" was just the relative speed between any two objects in different inertial frames so they should really be called the EINSTEIN TRANSFORMATIONS, but that is history too, and I digress. Anyway, in applying the transformations between different internal frames, it must get pretty complicated to decide where the all the factors go considering history of the objects must be taken into account & the fact that different objects could have all kinds of wild acceleration histories! A: Ummm... Q: Hey, what about a TRIPLETS Paradox? Suppose one triplet stays stationary while the two triplets accelerate away from her for the same time period (relative to her, no doubt) but in opposite directions???? Once all of them are in inertial frames (no longer accelerating), it follows that, having motion in opposite directions, the two TRULY moving triplets must have speeds relative to each other that are even greater than that relative to the stay-at-home triplet (I'd say we should add the two speeds, but that probably wouldn't be Einsteinian)! Can the Einstein transformations handle all these situations without contradictions??? A: I've got to go. Q: Thanks for clearing all this up for me!

Can the apparent acceleration of an object without internal stress be explained without invoking a global (“fictitious”) force?

Dialect, I think the only one who doesn't have a clue and is confusing his viewers is you. Would you like to feel the rush of acceleration driving a sports car? No need my man, someone else with a sports car can accelerate away from you and by your logic it will be the same thing.

I'm curious as to know, as a lot of commenters have raised here, regarding the relativistic vs absolute nature of forces and acceleration, which seems to be the fundamental issue most have with this explanation?

I might be very wrong here, but if one assumes Newton's third law an an axiom, isn't an inertial frame of reference definable as a frame in which total momentum is conserved?

What quantum mechanical process governs the rate of the harmonic oscillators (clocks) and how is that process affected when acted upon by an external force which results in damping of those oscillators?

Maybe the issue is that others are equivocating acceleration with the experience of force? If we define acceleration in purely coordinative ways, then yes, both twins are accelerating. However, only the twin on the spaceship is experiencing the actual inertial force of the acceleration that occurs at the turnaround point. If I'm going 40mph down the road on my bike and hit the front brakes too quickly, it's gonna be me who goes flying over the handlebars; the kid standing still on the sidewalk watching me wipe out isn't going to be pushed over onto the ground. Acceleration may be relative, but force is still applied only locally. If the solution to the paradox is to find something about the twins' situations that are asymmetric, that to me seems like the most obvious thing to look at.

OK, your main point is wrong. Acceleration is not relative. That would violate the Equivalence Principle. It would mean that the existence of a gravitational field is relative, and it isn't. But you don't need general relativity to see the problem. An accelerated observer is able to verify that he is indeed accelerated using purely local measurements. Just look for violations of Newton's First Law. Experiment with a particle experiencing zero net force and determine if it nevertheless seems to accelerate. If violations of the First Law seem to exist, you are accelerated. The Earth observer does not see such violations so he is not accelerated. "All motion is relative" is true, but you cannot obtain from that the conclusion that acceleration is relative. It is not. You cannot turn an accelerated frame into an inertial frame by a simple Lorentz transformation.

I have a question. I learned about time dilation using the “time clock” experiment. It usually contains one time clock in a rocket and other stationary. The question is woudnt the person in rocket see the stationary clock in motion? Wouldnt he come to the same conclusion that the other clock is slower? Both the observers can claim that the other clock is slow. Which means we can never be sure who will experience slower time. This doubt makes me doubt the whole time dilation thing. Poz help.

Why is the +x twin Lorentz calculations not providing the same answers as the -x twin since they are perfect mirrors of each other? Seems to be another problem in the main problem, if the result depends on the direction of the speed, which is completely relative!

You've not studied general relativity. If you learn that, you'll have a better understanding of acceleration. And then twin Paradox may seem to settle

I stopped watching your video the moment I heard your assumption that acceleration is relative. No, it isn't as the person being accelerated feels the acceleration, it feels like an increase in gravity whereas the person left behind does not feel any acceleration (any increase in gravity) at all.

Nice video! When's your next video?? I'm itching to know more!