Do Inertial Frames Resolve The Twin Paradox? 

Knowledge cannot resolve the twin paradox; either twin B is older than twin A or they are not. This means that there must be something physically different between A and B despite each having the ability to claim they are the twin at rest. A and B begin in the same inertial reference frame. Next, the twins move apart and then back together. Finally, twin A is found to be younger than twin B. What can be surmised about the difference between what happened to twin A and what happened to twin B? Twin B did not undergo a force accelerating them to a "faster inertial reference frame from when they were at time 0; only Twin A did. We know this because Twin A's clock has run slower (experienced less time) by comparison to Twin B's clock when they are brought back to the same point in spacetime and compared. Thus, relative acceleration to a faster inertial reference frame (from the imposition of a force) is the cause of time dilation. Can this tell us anything about General Relativity as well? Spacetime is curved by the interaction of masses. The greater the sum total of masses interacting, as well as the lesser the distance from each other, the greater the curvature between them. Also, according to General Relativity, the closer to the center of the greater mass, the slower time passes which suggests that spacetime is not merely curved, it may be infinitely extensible, and actually flowing towards mass; however, the greater the mass, and the closer to its center, the faster spacetime flows and the slower time passes. The lesser the mass and the further away one is from the center of mass, the slower spacetime flows through mass, and the faster time passes as the mass is accelerated through spacetime. In other words, the speed with which one moves through spacetime relative to an initial inertial reference frame will determine the local passage of time relative to the initial inertial reference frame. The key thing to remember is that there is no absolute inertial reference frame of spacetime, but there are relative inertial reference frames with respect to an initial inertial reference frame.

@Dialect, I'm watching your videos in order, and with this one I'm wondering why nobody is pointing out the obvious asymmetry, which is that the younger twin will have some of his mass missing. Acceleration of mass isn't possible without sending a certain amount of mass or energy the opposite way. If we assume that the twins have perfect rockets that can accelerate with 100% efficiency by shooting light in the other direction, when the twins converge again, they shouldn't compare clocks but mass, and I would bet that the missing mass of the younger twin is exactly the amount of time he's younger by, if you convert that mass into time via e=mc^2. It also makes sense since if a twin shoots a small amount of mass, he'll age less since he'll accelerate slower, and more if he uses more mass.

Hey, Idk much as I am an eng. student ,but here is something : The one who is aceelarating/feeling force can make a difference. How ? Say they guy on the flight which takes off has juice in a glass, the.liquid is then going to make a tilted shape, as long as the acceleration exists. but there will be no such effect on the stationary twin's side. This distinction can be made by anyone (stationary or.moving twin).. and thus they cant say that their perspectives are equal. There is a clear difference between which is inertial and which is non-inertial.. even if the entire universe didn't exist for any reference.

Again, as I said in the other video: the accelerating person will feel the acceleration, the other person will feel nothing. Acceleration is not relative. Perhaps "feel" doesn't sound scientific enough (although it is) and could be replaced with a very effective accelerometer: a ball being tossed up in the air. Both persons will see a quite different effect. So, you can't use this erroneous relativity as a basis for your reasoning.

If you are going to solve this with sr, an acceleration is NOT relative, it is absolute. At least make an attempt to understand the topic before spreading this kind of misinformation. This is pure conspiratorial denialism. That said, all the examples of explanations you are showing that you say are disagreeing all give the same explanation. The asymmetry is because there are three inertial frames of reference: one for the twin staying at home, one for the travelling twin as he is going away, and one for him going back. The Lorentz transformation can be done for any of the three (we can view this considering any of them as stationary) and they will all agree on which twin ages more. It is, however, not the acceleration itself that is causing the difference, it is going from one inertial frame of reference to another, which you inevitebly do when accelerating.

The last part on Emmy's being confused is irrelevant 100%. It does not matter if she does NOT understand who is aging faster or slower for the paradox to be solved.

Ok here's a cheeky solution, assuming that quantum field theory doesn't go out of the window, the accelerated observer will feel Unruh radiation, whereas the inertial one won't. So there is theoretically an experiment that both observers can do (carrying a very acurate thermometer) to decide who was inertial. Or another way to say it is this, which does not assume a quantum field, just relativity. Smoothly accelerating frames have an event horizon. There are experiments to be done in order to infer the existence of these horizons in the case of the accelerated observer. Now, you can chose to draw the stationary / inertial observer in an accelerated coordinate frame. But the inertial observer would not experience the phenomena. So the accelerating observer would compare their calculations to what the inertial observer experienced and see that they were accelerating, but the intertial observer were. Furthermore, there is the case of pedagogy here... in so many iterations of the twin paradox we introduce extra descriptors, such as rockets, that have a shape that break the symmetry, a human anatomy, intuitions about a front direction and a back direction... Furthermore, many present the diagram as if the accelerating observer is moving with constant velocity and only "turns around (i.e. accelerates) at some point. This way, there is an almost instantaneous impulse force at the turning point. But it might be pedagogically better to talk about smoothly accelerating and decelerating observers, and observers who do not have distinctly human anatomy or use familiar space propulsion. In the end, what solves it is the understanding of inertia.

If Albert throws an apple towards the bottom of the spaceship, he will see the apple apparently move to the side as well (relative to his ship), while he is not in an inertial reference frame. If Emmy does the same, she'll never experience such a pseudo-force because no coordinate transformation will establish such a pseudo-force (only on the apple and not on the ship). If your "acceleration is relative" claim were true, Emmy's apple would somehow have to be linked to Albert's ship so that Emmy could experience the pseudo force as well. Only then the situation would be truly symmetrical. How are you suggesting that would work? Your videos are very well produced and it is great that you are sceptical, but you seem to be closed to accepting the very simple fact that it is possible to distinguish inertial frames from non-inertial frames without resorting to a third reference frame (e.g., an accelerometer calibrating place on earth). BTW, your epistemological route (speculating what observes need to know) is a complete dead end. Consciousness and knowledge does not come into this at all. If apples were automatically pushed towards the spaceship bottom, one of them would bounce against the back of the spaceship and the other would not. Physics does not need conscious observers.

He is apparently, IMO, confounding coordinate acceleration and proper acceleration, or he considers proper acceleration to simply be coordinate acceleration. They are not the same or defined the same way.

Inertial frames are defined by whether systems in that frame obey newtons' first law. Systems in a non-inertial frame do not. An experiment can be done in the frame to check. For example throw an object perpendicular to relative motion of the rocket and earth and see how it behaves. If an object is thrown up on earth this object will always move straight up in both frames relative to the earth. Even when the rocket is accelerating. However if the object is thrown on the rocket during the turn around it will follow a curved path relative to the rocket in both frames, showing this frame is non inertial, not the earths. That's how you can resolve the problem either using inertial frames or acceleration being absolute. The original explanations are not wrong but this is.

I think I see the problem with this video, what people claim is not that acceleration is absolute is some mystical way, but that you can't differentiate from different inertial frames. Although they do imply the same things, they sound much different, and you tend to think about things the wrong way too if you start with the first statement. The problem with acceleration explanations does not lie in representing things with coordinates. Thats not even a problem to begin with. You have to differentiate inertial reference frames with accelerating ones. Something can't tell what inertial frame it moves in, what velocity it is barreling through space in, relative to this or that. All it can tell is if it's accelerating or not. Let me clarify on that. All things moving in an inertial reference DO agree on the laws of physics. If the frame of reference IS accelerating, the laws of physics will be different, offset by that acceleration. In the example of you spinning yourself, if you observed the laws of physics while spinning, they would be different that if you weren't. I think its a fairly arbitrary choice that we choose the laws of physics to be one when people are not spinning or accelerating. But it's a fair choice because it makes things easier and because of the fundamental fact that you can't tell what velocity you move at, what inertial reference frame you are in, but you can see if you accelerate, again, the laws of physics change accordingly. You can't ask why it's like that because all people can say is that it's from observation. If inertial reference frames had the same properties as accerating one, the laws of physics would be different. The answer was acceleration all along igues

I believe Prof Johnson from Fermi labs has it correct. It is being in two (or more) reference frames that causes the time to slow relative to the twin that was in just one reference frame. The example just using clocks on already moving frames/rockets demonstrates the point quite well. Acceleration (or force) is just a means by which a twin could change velocity and therefore reference frames. Knowing the amount and duration of that acceleration, however, is not enough to determine how much time dilation occurred. The acceleration only gives you the velocity difference, not the duration of the difference, which is what you need to calculate the net time dilation. The need for this additional information demonstrates that it is not the accelerationn itself that caused the time dilation. You only need to know how long the second twin was in each different reference frame (and the velocity difference). As to the question how does one determine if you are in a difference reference frame? This does not seem so hard. Different reference frames are identified by simply determining whether the distance between two objects is changing. That is all you need to know. Two objects in the same reference frame will maintain a constant distance from one another. Otherwise the distance will change. Again, you don't need to know or even have acceleration to calculate the time line difference between two paths if you just track the clocks it the two reference frames. This is the example of Prof Johnson of Fermi labs gave, where you simply perform synchronization of clocks when objects in difference reference frames pass each other thereby negating the need for physical acceleration. The same time delay will be seen in the clocks just tracking the time that passed in the two reference frames vs the clock in the single reference frame.

Twins Paradox INTRODUCTION: The Twins situation is not paradoxical when the equations are used properly. The only valid equation for time dilation is the Lorentz Transformation, and the only variable it contains is velocity; and this velocity is not a relative term, but an absolute one. Therefore, the twins must not only agree on a “common” frame of reference, but agree to an “accurate” rest frame of reference. REST FRAME OF REFERENCE: We are aware of a “universal” rest frame of reference based on the dipole CMBR (Cosmic Microwave Background Radiation). Although not guaranteed to be the “true” rest frame of reference, all evidence supports that it is and until it is proven false it can be accepted as the “true” rest frame of reference. According to the Lorentz Equation any object at absolute rest will experience the greatest length of (true) time. The velocity of the sun relative to the CMB rest frame is 368 ± 2 km/s towards the constellation Leo, equating to a Lorentz Factor of 1.0000007534 for our Sun. Meaning that the sun loses 24 seconds per year or almost 40 minutes per century. The Earth twin will lose only 3.4437 minutes during the course of the 8.7 year experiment compared to the rest frame of reference. The Twins Experiment will consist of one twin in a spacecraft instantly accelerating to a constant 99.995% c towards Alpha Centuri A, sling shooting around its gas giant to return home, then instantly decelerating about Earth’s orbit. The second twin will, of course, be “stationary” on Earth’s surface travelling at 368 km/s (0.123% c) towards the constellation Leo. The first twin will be in free-fall the entire trip, including the sling-shot maneuver, and believe that he is in an inertial frame of reference. The second twin will feel the Earth’s gravity and perceive himself to be in an accelerated frame of reference. Rest time Event Earth time Alpha Centuri Spacecraft (days) (days) time (days) time (days) 0 Spacecraft leaves Earth 0 0 0 1,588.806072 Light of departure reaches Alpha Centuri A 1,588.804875 1,588.804875 15.887862 Light from spacecraft departure is visible 1,588.804875 1,588.885516 Spacecraft slingshots around Alpha Centuri A 1,588.884319 15.888657 Light from spacecraft slingshot is visible 3,177.689194 3,177.771033 Spacecraft arrives at Earth 3,177.768638 3,177.768638 31.777313 Light from spacecraft arrival visible 4,766.573513 Days lost compared to “rest time” 0.0023941260 0.0023941260 3,145.993719 CONCLUSION: The twin situation only becomes a paradox when the “true” fixed frame of reference is replaced by a “false” self-centred one; a concept that was disproved with Copernicus and should have been eliminated. Acknowledgment that one is not at the centre of the universe and proper use of the Lorentz Equation eliminates this paradox.

I respect what you're trying to do, i.e. establish that acceleration is not absolute, but I can't help but feel something or another is being overly complicated. From my limited understanding, acceleration doesn't have to be absolute to conclude that 'space twin' ages slowly. It just has to be, uh, 'locally(?)' defined for the two twins' reference frames (inertial or not). Personally, to avoid complicated stuff, I just picture a suspended object within each ship that are both hanging in the same way to establish that both ships are in the same reference frame. As long as both experience no acceleration, the way the object hangs won't change. So even if the entire rest of the universe is just empty space, there is a way to tell which ship accelerated, at least relative to both of their 'initial' reference frames. What I'm trying to say is, neither of the twins are 'agreeing' that one is accelerating while the other isn't. Acceleration is not absolute. One ages while the other doesn't because one of them is changing their reference frame from what it used to be. They're aging differently from what they would have if they *didn't* change their reference frame. Twin A doesn't see B accelerating away and neither does B see A accelerating away. The acceleration is not relative to the other twin but relative to their own prior reference frames. Hope I was able to make my point of view clear.

Could there be an asymmetry in the fact that, to turn around, the « moving » observer has to eject gases in the opposite direction ? In that case, the « static » observer hasn’t changed over the course of the experiment, while the « moving » one has splitted between the space ship and the emitted gas ? It means that both observers never really meet again, as a fraction of the « moving » observer is still moving in the opposite direction and never has a chance to compare clocks with the « static » observer

To state your point clearly, you should tell which assumptions you accept. It seems that you are only assuming the postulates of special relativity, in which case I see where you come from: how do we differentiate whether object is accelerated or the whole universe around that object is accelerated. Although this can be experimentally tested by accelerometer, the postulates of special relativity alone don't tell in which reference frames the accelerometer should be in rest (i.e. show zero acceleration), hence we have not really disambiguated the symmetry. You then reduce the universe into two objects. However, if there is nothing else in the universe and these objects are indivisible, then there is no way to have acceleration as it requires exchange of momentum. Hence, to perform the twin paradox you need slightly more complicated universe (at least three objects), in which case the frames of the twins are not symmetrical, hence the paradox can be resolved. Conclusion: you cannot isolate the problem to only containing the twins, as (at least) one of the twins should somehow interact with the rest of the universe for relative acceleration between the twins to occur. In the usual description of the twin paradox, the cause for acceleration is abstracted away in such a way that the other twin is in rest throughout the experiment. You seem to try to get rid of this abstraction, but doing so you must describe the system more fully than only the relative positions of the twins, which would disambiguate the symmetry.

If the twins calibrate their identical accelerometers before departure, then only one will measure an acceleration. How is that not the asymmetry? I don't understand why you didn't address this.

Why are people talking about acceleration when the "paradox" is all about time and distance (that form the spacetime Minkowski metric)? The stationary twin can have infinitely many accelerations and rest frames if she just walks in circles when waiting her twin to return. But note: the stationary twin travels a straight line in spacetime, whereas the travelling twin does not, hence the *proper time* of stationary twin between the start and end points (in spacetime) is more than of the other twin (who travels more in distance).

Assuming, for the sake of argument, that one frame experiencing force while the other frame isn't experiencing force is all that's necessary to break the symmetry, then it wouldn't matter if any observer knows which one is the one experiencing force. The solution, then, would not rest on any one "knowing" which twin will be older, only that one of them "will be" older, because that twin "did" experience force whether they knew it or not.

So good to have another video from you! More of them please!

9:58 your argument about requiring prior knowledge to determine an inertial reference frame is ridiculous. All of physics requires prior knowledge, science is based off of testable observations. You just say this is order to claim that forces are relative which is a claim I have never heard from any other scientist. Maybe instead of asking other content creators to update “false” claims you should begin by doing so yourself

Can you explain why my thinking is wrong? My instinct would be to dispense with the notion of acceleration and instead say that F = (mv)/t. Therefore, the twin can be said to experience a force only if its momentum changes. However, because momentum is conserved at every instant there must be some other mass which all observers will agree changed momentum at precisely the same time as the twin. I think that means that this supposed third mass must have negligible spatial separation from the supposedly accelerating twin, at the moment of momentum shift, otherwise there will be disagreement about whether or not the twin and the mass changed momentum at the same time. So now let us go back to empty space with only two twins. The twins are moving apart at .5C (or whatever). Then that situation reverses and they are closing the distance at (.05c). The question is which twin (it can be both but lets set that aside for a second) experienced a change in momentum. Well, if Alice says it is Bob, then she is required to find Bob's momentum-balancing mass somewhere in the universe. Shouldn't be hard since it will be the only thing besides her and Bob. Same thing for Bob, he must find Alice's momentum balancing mass. Off-the-cuff it seems like there can be no disagreement because any alleged momentum balancing mass must have the opposite momentum of the twin for whom it balances. But, I something feels not right about that. Perhaps it is the difficulty in measuring the momentum of a mass that is now far from them? In any case, I think demanding that the momentum balance be shown to have changed momentum at the same moment that the twin did pins it down because the mass must be in the same place relative to the twin as measured from both frames of reference. Side note: As a quick heuristic, if the twins are the only objects in the universe then when they meet again, one is likely to be missing some of its mass. So that is the guilty party. I say likely because I am not 100% certain that the only available balancing mass is some mass that once a part of the twin's ship but it certainly seems that way.

This is the best videos i have seen on this subject. Hope you make plenty more videos my friend👍

So, if I am understanding correctly, the essence of your argument is that because acceleration is relative to your inertial frame and the forces required for acceleration are impossible to objectively measure, there is no way to tell which twin will experience time dilation relative to the other. So, is the goal of this RU-vid series to point out that this is a serious scientific and philosophical problem, or do you have a solution that you are leading us toward? We know that ONE of the twins does experience time dilation, so there must be something that make the situation assymetric. Or, the assumptions about acceleration truly being relativistic are wrong. Your videos are really well done, and you obviously have a solid background in physics and philosophy. But has anyone in proper academia touched this subject in the same way you are? This is just such a famous problem that it would be wild if it remained without a solution and these are original ideas you are bringing up.

The true solution to the twin's paradox is that in the usual example the twins are taking different paths through spacetime, and these paths are not defined using coordinate systems, so they remain the same in all reference frames. This means that the arc lengths of these paths would in general be different and invariant and since the proper time elapsed for each twin is defined as the arc length of the paths each twin traced, which are timelike, this means that each twin will measure a different proper time passing compared to the other twin when they reunite.

11:13 An observer doesn't need knowledge about the sources of a force in order to observe the effects of the force. The laws of physics play out regardless of who knows what. What knowledge exactly do you mean anyway? 12:05 What exactly do you mean by "defined globally" and "defined locally"? When twin B bounces off an obstacle (for example the particles of the burning rocket fuel), his speed changes in any inertial frame of reference. I don't understand what you consider problematic about this explanation.

There is a way to resolve the paradox without any accelerations or forces, and to isolate the 'switching' of frames, but it involves triplets not twins. Consider Alice, Bob en Chris: Alice stays on earth, Bob leaves Earth with velocity +v and Chris is approaching Earth with velocity -v. All velocities are constant w.r.t. each other, no one is accelerating. At some point P Bob and Chris pass each other, both keeping their constant velocity. At a later time Chris arrives at Earth, completing a triangle in spacetime with Bob and Alice. Here are three inertial frames. Now, one could calculate the proper time B of Bob’s interval from earlier Earth to meeting point P and the proper time C of Chris' interval from P to later Earth, and add them together to find out that the result is shorter than Alice’s proper time. But -- one would be adding a value from ONE inertial frame to a value from ANOTHER inertial frame. As none of Alice, Bob or Chris is switching frames, who is? It is WE, the ones calculating, who switch from one frame to another. We are adding apples to oranges, so to speak. Normally, adding two values from different frames does not have a physical meaning but in this case the two intervals share an endpoint (P) and together form a potential single trajectory. This actually makes the prediction that, were a single entity to traverse the trajectory B + C (with reflection at P) it would experience a shorter proper time than A. The important fact here is that Bob and Chris stay in different inertial frames, irrespective of what inertial frames ‘fundamentally’ are. Neither of them switches frames, it is we who are adding things from different frames, getting a surprising result. N.B. All this hinges on the assumption (fact!?) that two inertial frames being different is an absolute. I don’t see how Bob and Chris could occupy the same inertial frame especially going in opposite directions at their meeting point P.

Great video! Do you have a solution that you came to by your self? I was struggling with the twin paradox for a long time before sitting down and thinking about what it meant to accelerate. I realized that you need a source as you mentioned in your video, so I guess that I'm in that thought camp. One thing I'm confused about with your issue is that you stated that if the observer can't tell who is interacting with a force field then since they don't know then it would change the result. How would it do this? Since in theory, there is always a way of detecting who is experiencing the interaction then doesn't this mean that the time dilation will always occur to the observer who is interacting with the field. Why would our ignorance matter?

To be fair, Don's exposition (FWIW, he follows the Wheeler & Taylor book) is misrepresented. No mass is involved, and thus nothing experiences acceleration in this thought experiment. The experiment setup involves three relatively inertial frames, each containing a clock at their respective origin. With respect to the frame A, frames B1 and B2 move with the opposite velocities along a single axis, such that their origins meet pairwise with a zero spacetime separation in three separate events. The initial conditions are such that the order (that would be agreed upon by all inertial observers, naturally) of these zero-separation events is: 1. B1 coincides with A. At this moment B1 reads A's clock and resets its own clock to the same value ("twins separate"). 2. B2 coincides with B1. Similarly, B2 resets its clock to the B1's clock ("twin B instantly reverses its direction"). 3. B2 coincides with A ("twins reunite"). At this moment, clocks in both A and B2 are read and compared. In other words, there is no caricature (and massive) Einstein physically jumping from B1 to B2. Each event coincides in spacetime with the origin in each pair of frames, and only involves transfer of information, not of mass; the whole setup is entirely kinematic. Note that none of the frames can be designated "privileged" in any sensible way.

Wow I m really waiting for your video And glad to see you uploaded :) Never stop uploading

I really enjoy this channel. It helps me understand the concepts by exploring faulty reasoning and challenging me to figure out what is wrong or missing. ..or is it?

I think you will find that different videos bring "different" solutions depending on what details they think viewers will want to see.

Can't we define an inertial frame as one in which an accelerometer reads zero? If not, what does an accelerometer measure?

"Acceleration is, by definition, a purely relative affair." Proper accelerations (i.e. - local accelerations that cause deviations from inertial movement) can be measured without any reference to any fixed external frame. If I put you in a black box floating in space above Earth and then start applying an acceleration to it, then your box and you will experience that acceleration and you can measure it without reference to any fixed external frame. Furthermore, if I begin to apply 1000 g's of acceleration to your box for an extended period of time, then you will be turned into bloody pulp and you cannot correctly assert instead "No, it was actually the other twin that was accelerating (and experiencing forces/accelerations) away from me instead." I still *REALLY* don't understand how you can be getting something this obvious and basic wrong. To your query about building an accelerometer without any preexisting knowledge of your motion, that is easily done. Get / construct a bunch of equivalent springs. Attach one end of the springs to the inside of a hollow sphere whose radius is somewhat larger than the springs' length when they aren't stretched. Then attach all of the other ends of the springs to a mass such that the forces of the springs on the mass should all cancel one another out (i.e. - pair them up so that the line along each pair of matched springs goes through the center of the mass + sphere). Thereafter, If any of the springs stretches differently than the others or, equivalently, the central mass deviates from being perfectly centered in the sphere, then you are not in an inertial frame and are experiencing forces / accelerations. From the particulars of the stretching / central mass deviation, then you can determine the direction of your proper acceleration and have some rough notion of its magnitude (e.g. - more vs. less). Most importantly to this conversation though, you can easily determine whether you are in an inertial frame or not and none of this requires calibration to an a priori known inertial frame. EDITED - for a clearer and more concrete description of a universal accelerometer.

I have 2 clocks together and synced. I move them apart in a completely mirror image of each other and then bring them to rest at a distance, again, in a mirror image way, and they both stop running and show their final values i.e. all accelerations, decelerations and constant velocities happen at exactly the same time and for the same duration in opposite directions. Relativity says one must be slower and the other advanced - but which one is which? From the frame of reference of the starting point, both dilated identically and are thus still perfectly synced? From the frame of reference of either clock however, the other clock is slower? ?

I don't think the analogy of observers understanding why one ship is moving is properly used here. Chemicals don't know chemistry and, still, they act according to a very complex set of rules. The hypothethical example where the particles are the only thing in the universe leaves out how can they accelerate and change directions in the first place. Things that get forces applied to them leave traces besides them accelerating.

Excellent! Keep up the good work!

Wait a second. In the previous videos, I took your statements about how things resolve if the observers agree as a figure of speech. Are you suggesting that the resolution of the twins paradox depends upon the opinions of the twins? I always read the problem as meaning that IF A measures, he'll find this; if B measures, he'll find that. But I didn't think they actually had to measure it. Are you saying that this is an example of the macro world relying, like quantum, upon measurement? Somehow I don't think that's where your argument was leading. I would have thought that the physics doesn't care what the twins think - the fact that WE can measure things from both points of view, and that we can establish either twin as our reference point, grounds the paradox. If the twins were selected from among the youtube speakers your criticizing, who ignore the basic relativity of motion and acceleration and therefore agree that B is the one who accelerated, that should change nothing. When they meet, one should appear older, and the paradox then arises. If we tested this in practice, we don't know what would happen. But they would see - something, there's no getting around that. Or are you genuinely asserting that opinion and measurement change what they would see if they followed the dictates of the test and then actually met, in the real world?

could we resolve this with each pilot just being a single charged particle and see if it emits EM waves? also, if its a hydrogen atom, we could see a lag in the electrons wave function before it responds to the protons EM field, or vice-versa, if it undergoes acceleration, right? i get that force isnt truly felt, just interpreted, but dont these particles have fundamental properties that could always determine which one actually went non-inertial? or would your response be something like "how does the EM field know that particle moved and not the other particle?"? ill admit im thoroughly puzzled. in the macroscopic sense, it seems easy to use accelerometers. but if we go to 2 truly neutral, fundamental particles in flat, empty spacetime, there is no way to establish which clock should tick slower.

How can acceleration be a "relativistic" matter if one can even die from acceleration big enough? Let's imagine a thought experiment where Albert accelerates so fast that he dies from too many G. From his point of view, taken as "immobile", he lives and Emmy dies because of this super-killing acceleration. Does it make him Shroedinger's Albert then - alive and dead at the same time? Also, Albert does not need to have any knowledge at all to die from "too many G". He can as well be infant!Albert, placed in the rocket at birth, and still he will be killed by too big of acceleration all the same! And he could even be a clock sentimentally called "Albert" and STILL be destroyed by acceleration. It is NOT "uniform changing of all the speed of all the rocket", rocket is a non-absolutely rigid body that undergoes acceleration NOT "all-at-once".

Tremendously interesting. Long held questions. But, if I got this right. Twin A in her space ship sees her twin B flash by going constant .99 c. Twin B travels out , say 5 ly, and slams on the retros to a screeching stop and turns around back to Twin A. it makes no sense to me that his one moment of stopping (deaccelerating) instantly changes B's age relative to A. Or what about B not stopping, but making a long winding loop (keeping v constant). Are we now going to rely on the acceleration due to change of direction? Thanks. Keep it coming.

I think I clearly belong to the apriorism camp tbh, and I don't think you need extensive physics knowledge to "feel" if you are accelerating. It is true that we have to introduce fictious forces to account for the acceleration of one frame of reference with respect to the other. Introducing those fictious forces is a symetric process to describe the movement, that is introducing them to describe Emmy's movement in Albert's frame of reference is just as valid and will yield the same results as using them to describe Albert's motion in Emmy's perspective. However, if it is Albert who fires his rocket, he will be the one clearly feeling the acceleration. It doesn't require physics knowledge, just like a kid in a car feels the acceleration and his helium balloon will move towards the front while he is pushed back. You can mesure stress being induced in the materials. Now that I think about it, what if a planet just appeared behing Albert and its gravity would make him accelerate and then disapeared, ie, what if all Albert's molecules were subject to the same force, what would he feel. I may not have understood your point completely so I'll watch the video again and keep pondering about it though.

So, is Dialect right and the rest of the RU-vid Twin Paradox videos wrong? Do I have to figure out this myself?

Wierd argument about feeling force. You could argue then that vision is a sense too, so how could you tell that someone is moving reletive to you if you can't see

7:50 I don't agree that there is a problem even if you remove the rest of the universe from this thought experiment. You still have a universe but the matter in this universe is composed only of these two observers and their spaceships. Their center of mass is necessarily in linear motion (or at rest) and doesn't accelerate (though I'm not sure how easy it would be to measure the location of this center of mass). Even if one of the observers accelerates it doesn't cause the center of mass to accelerate because his spaceship can only accelerate by chugging some reaction mass in the opposite direction.

Hey dialect, For me, this was a great video, and very mind-opening. It made me understand the solutions for the tween paradox better and see that the proposed solutions are not really as firm as they claim to be. I saw you ending the video with a question mark regarding the cause for the break of the symmetry. I have an interesting proposal, though it is not fully developed. I have found it working quite nicely to solve other inconsistencies with the theory of relativity. It lies in a little different interpretation of the principle of consistency of light. While Einstein proposed that the speed of light is independent of the speed of its source, and travel at the speed of C in relation to every observer, My proposal is that the speed of light is independent of the speed of its source, and travels at the speed of C in relation to space. This means we treat space as an absolute reference frame. Once you do it, it is easy to see that the symmetry is broken as one of the tweens is static in relation to space while the other one is in movement. This proposal also predicts that if you give different values to the relative speed of the "static" observer in relation to space, you will get different results for the paradox. You can even get a result where the moving twin ages more than the static tween. I don't think this prediction cancels out this solution, as I don't think we have had enough tween paradox experiments, to account for different initial conditions.

I think the only problem here is that the concept of force is not well-defined. So to put it more concretely, I would like to use the phrase 'interaction'. An interaction is a binary relation between two fundamental particles that make up all the matter and energy. Binary relations are absolute and universal, not dependent on any frame of reference. A fundamental particle that is free from any binary relations defines an inertia frame of reference, any reference frame that is moving relative to the inertia frame by uniform velocity is also an inertia frame. Newton's third law simply states that any binary relation is symmetric. Now we define an equivalent relation for any two frames of reference to be equivalent if and only if they are in uniform relative motion with respect to each other. Special relativity simply states that any equivalent class only has one set of equations that governs how a physical system evolves.

Thank you Dialect, for this video and the previous one. I'm still a skeptic though. Here is what I'd like to see, and hopefully you can address it. A double-blind twins experiment: A pair of large windowless space stations, each with a twin and a clock. One space station will rotate to produce 1G without any other noticeable effects. The other space station will accelerate away at 1G to a great distance and then return. Neither twin will know who is rotating and who is moving away and back. The moving station will have to make two acceleration changes at prescribed times to complete the return trip. The rotating station will make equivalent acceleration changes at identically prescribed times according to its own clock. So that neither twin could know if they were moving or rotating. When the space stations reunite and compare clocks, how will we know which space station accelerated away and back, and how will we know which space station stayed in position and rotated? How would a rotating clock at 1G differ from the one that traveled great distance at 1G, if we couldn't be sure to know which was which? We could have even more information in this scenario. Say we could know the distance apart, but since each twin on each station would feel the exact same acceleration and never know for sure which was moving. My thinking is that we can never know who is moving, and that when the clocks are brought back together, they will have to match the exact same time. It makes me think that SR can not answer the problem, and that GR is required to answer the problem. GR equivalence would produce clocks with matching times. I would genuinely like to know how others would answer this. Thank you.

Actually, speaking of moving at a constant speed relative to the rest of the universe introduces the absolute frame of reference at rest, which is forbidden by the special relativity postulates

I would argue that physics education would not impact force resolving the paradox. A force will still exist weather someone knows how to detect it or not, therefore they twins would witness time dilation but not really know the difference that produced the outcome.

Could you defeat the "acceleration/reference frame" arguments by asking what happens if both twins fire their rockets away and fire their rockets to return making them perfectly symmetrical? Does this scenario deviate from the twin paradox? Does time dilation change if you are moving toward vs away from each other? Please excuse my ignorance and thank you for your patience in your responses.

I guess I fall into the Apriori camp, but I don't consider knowledge to be the thing that causes a frame to be inertial or not. Knowledge (and an unambiguous definition of an inertial frame) is merely what allows us to identify which frames are inertial. So we certainly can replace the observers with systems of inanimate particles. And the system that is not inertial is the one that undergoes deformation. It is the system whose parts do not all accelerate at "exactly" the same time, the system whose parts propagate the change in motion through the system as a wave. Now, as to whether or not this and this alone should solve the twin paradox is a different matter. I, for one, think the "real" solution is that Special and General Relativity are a bunch of BS.

@Dialect I am probably thinking about this incorrectly, since I know only the basics of relativity, but this is what I think. You probably already addressed an objection like this elsewhere, but maybe not. Maxwell's Equations should create electromagnetic waves that propagate at a constant speed and direction in spacetime. Hence, light could be used to find an inertial reference frame. For example, let's say Alice is on Earth and Bob is on a spaceship that is initially stationary, but accelerates at time t=0. Suppose that in the spaceship, there is a mirror along the x-axis, and a laser at (0, -1) pointing in the positive y-axis, normal to the mirror. Both of these measurements are done relative to the center of the spaceship, but no matter what point of reference you use, the laser should remain perpendicular to the mirror (even if this is not quite accurate, it shouldn't ruin the scenario). Suppose Bob turns on the laser at time t=0. From Alice's Perspective: A photon of light will be emitted from the laser at that time, but the direction of the photon should not change until it hits the mirror and returns back to its starting position. But this starting position is now no longer at the position of the laser, but would be shifted left. If a detector was placed along the line y = -1 relative to the center of the spaceship, the detector should register a photon hitting at a point a bit left of the laser. The detector should measure light energy hitting it at a point left of the detector and progressing left along the detector. Because light is also a wave, an interference pattern should be visible left of the laser. From Bob's Perspective: A photon of light will be emitted from the laser. The photon hits the mirror and returns back to hit the laser. This is shown in the simulation I made here: www.khanacademy.org/computer-programming/light-particles-demo/5940491108532224 Clearly, these frames of reference are inconsistent, since the detector measurements must be consistent across reference frames. Hence, we have good reason to conclude that Alice is really the stationary observer. In the spaceships example, if the astronauts aboard each spacecraft set up the apparatus described, the detector can search for an interference pattern. If there is none, then the observer is in an inertial frame of reference.

I have a doubt: if we can measure acceleration with a spring inside the rocket without any reference frame, may we say that acceleration is absolute?

Even if we accept his explanation with inertial frame, external forces, etc, the question remains: why do the twins need to do different things? The paradox is meant to be symmetrical, i.e. both twins are travelling in opposite directions with identical rockets with identical forces, then both twins turn around to meet again. Who ends up older?

I get what you’re doing. And I like it. Sadly this will all be very unsatisfying though since the questions you are raising are not resolved. But it’s great to be introduced to what we did not know we didn’t know.

10:05 I think elementary particles are quite the experts in physics, so they have no problem "deducing" their own interactions and how to respond to them :). Like: "I got hit by a photon, I should adjust my coordinate system a bit". As long as "force" is due to interactions other than gravity (which is supposed not to be a "force" ) I dont see a fundamental problem. Or am I wrong? I would like to know if I am.

I was taught that the paradox is resolved by the fact that one twin leaves an inertial reference frame and returns to it, while the other twin never leaves. This video does nothing to convince me otherwise. What's the real answer if this isn't correct? Or are you saying time dilation isn't real?

I really like these videos, but still I would appreciate more if it focuses on what is the right explanation than on what is not.

Could you identify the inertial frames by reference to the Levi-Civita connection for the metric? Like, say that a reference frame is inertial when (a path in spacetime is a geodesic iff its velocity as expressed in the coordinates of that reference frame, are constant). Seems clear enough? Edit: I don’t understand the objection on the basis of “what if they don’t realize whether they are accelerating”. What does that have to do with anything? I think I don’t understand what philosophical question you are attempting to solve.

Thank you. I just could not get my head around different videos' explanations because they did not seem to resolve the problem. I'm so happy to see it's not because I don't get it but because the explanations are just not totally satisfactory.

Even though you refer to it you are ignoring the fact that real acceleration can be internally measured. Consequently, you can determine whether or not you are or not in an inertial frame of reference by internal measurements.

What would change if you replace the rocket with a free falling object? Like throwing an apple straight into the sky and catching it later. No rocket firering required for coming back. Who will be older? The apple, once released, does not feel any force. Not sure it thus sits in one inertial frame the whole 'fall'. And one might argue who is accelerating, i.e. changing relative velocity, the earth or the apple. And I'm also not sure if one now has to consider GR since the rockets are essentially replaced by gravity or curved spacetime ...

We might not know when or where it happened, but one or both worldlines must have been kinked at some point in the past due to a launch event. That's how you break the symmetry - with initial conditions. Waypoints are incidental. A worldline with no kinks runs parallel to the centre of momentum of the system and that's the context in which proper time runs fastest. Problem solved. Time to tackle the Andromeda paradox.

Sorry, this last "skeptic" part of the video is silly. The twin paradox has nothing to do with what the twins actually cognitively know, it only has to do with with what is theoretically knowable. The twins could be put in an induced coma for the entire time, and one would still age differently than the other. For that matter, you could have a clocks on board, but no people at all. Or Alice and Bob could be there, could make the wrong assumptions and come to the wrong conclusions about time and age. Embarassing! But it doesn't change the laws of physics or how much time has passed on either ship. The reason people refer to a force as breaking the symmetry and explaining the paradox is because...the force breaks the symmetry and explains the paradox, whether any conscious observers understand that fact or not. Though I actually agree with Dr Don from Fermilab that it's not actually the force that matters, but rather, the force is what causes the change from one inertial frame to another. It's the frame change that breaks the symmetry, as he explains really well and really clearly in his no-acceleration example with three observers instead of two.

In order to have a Paradox, first, you must have a variable speed of light by SR or GR. Take your pick.

Look at Spacetime as Sean Carroll explains it. Delete both axis in the spacetime diagram. Every observer or object has its own spacetime path and its own light cone. Besides. GPS should show there is no paradox.

This is starting to get a bit pedantic but I'll keep watching. I mean, come on. Let the two objects be two digital accelerometers which save history of second by second measurement and you'll know for sure that there is an asymmetry (if there is one). But I guess observing the asymmetry isn't enough. We want a why. Very well, I'll see what you have to say in the next video. My guess is it will come down to spacetime paths, as that's how it was taught to me. But I await the next one.

So ultimately, if you get rid of the universe, would both twins be the same age? However, if you bring a universe to reference who is accelerating, then is it twin B who is older?

PLEASE ANSWER Why is it considered that the twin that traveled returns with the clock delayed and not that he returned in the past of the first twin?

Simply put, pretty well non of the books nor videos reveal the "Absolute" cause of the "Relativistic" outcome. And so, how can anyone absolutely understand something, when the very concept of "Absolute", is being heavily heavily banned in the first place. Fortunately, there is one YT video collection that reveals the absolute foundation that creates the Special Relativity(SR) phenomena as an outcome. Plus it shows how even a high school dropout can derive the SR mathematical equations, including deriving the Lorentz transformations equations. The videos show you that all that you need for you to be able to find the absolute cause, is common sense, and the ability to place truth above mere beliefs.

@7:00 where did you get the idea "force is not an observable"? That's a slap in the face all modern physics and goes back to one I. Newton. These days force is interaction (particle scattering processes) so is "observable". If you are isolated from distant gravitons or whathaveyou (or gravity waves) you "observe" there is no force acting on you from without. By "observe" a physicist means "could be detected" not "is detected".

Question: if a twin is at rest and the other moves at constant velocity, who ages faster till the time moving twin starts to brake? Because both will observe the other one to move at constant velocity. so both should measure the other ones time to to have slowed down.

If you send a beam of light from earth to bounce off of an object 1 light years away, it returns in 2 years with zero clock change.

Everything I've ever wondered about regarding this paradox. But time dilation is real/measurable and fits the equations so it seems like SOMETHING has to explain the phenomenon. Maybe there are semi inertial frames formed by larger objects in somewhat fixed positions relative to each other?

The observer’s a priori knowledge determines whether or not the observer *understands* why the situation is not actually a paradox. Removing that knowledge doesn’t “recover the paradox”, it simply leaves the observer incapable of understanding why there is no paradox.

The laws of physics is the same in all inertial reference frame, but not in non-inertial frame. So if the laws of physics changes for you, that means you are accelerating. That's how you can tell which twin accelerated.

Arithmetic survives an lives together with self reference paradox. Why cannot Relativity live together with Twin Paradox?

Wow I finally understood the real implications of the twin paradox. I love your videos

In all those Minkowski diagrams about the "twin paradox" there is that time gap when simultaneity line suddenly jumps forward a lot. But if we take that kind of example, where twins send a message every year to each other in the speed of light, there is not THAT kind of jump in the receiving frequence in the spaceship. Only the frequence is bigger when the travelling twin is on his way back, of course. So, is that "time jump" real at all. That is something I don't understand (among many other things). Can you explain? A link to an example www.cpp.edu/~ajm/materials/twinparadox.html There is that time jump from 3.2 to 6.8 years on the earth If the travelling twin thinks only the messages and the time which the signal takes to reach the spaceship, he thinks that earth time goes faster all the time without dramatic jumps. Not slower first, then sudden jump, and then slower again. On the outbound leg he gets only two signals (two years per signal), eight when returning (after every half year), but he understands it is because the Doppler effect. Doesn't the amount and timing of the received messages reveal to the traveller (even before he is back at earth), that his time goes slower ALL the time and earth time goes faster?

"Another way of saying this is that at some point in the journey, one of the twins inhabits a non-inertial frame." I don't think that’s quite what they’re trying to say. What they're saying is that the traveling twin's journey can be seen as a combination of two *purely* inertial frames since you can model it with a scenario that involves two ships in inertial frames that move in opposite directions and exchange clock readings as they fly past each other. Although you could certainly argue that even in this scenario, acceleration and thus non-inertial frames were required for each ship before the experiment began and that perhaps that’s what made the difference. Also, I think you worry too much about epistemology. You should just replace all pilots with autopilot systems and stopwatches and stop worrying about what the people in each reference frame believe. This is physics and the laws of physics don't care about beliefs. All this talk about what the pilots can induce muddies the waters and makes things more complicated and confusing than they need to be.

I think I belong in the Apriorism Camp except I would, first of all, complain at your statement "An inertial frame is not being acted on by any known force-producing sources" This is an absurdity because an inertial frame is a set of points. Points are not entities with mass, and cannot be acted upon by forces, whether known or unknown. There is no "pretty big hole" in this solution because there is no need to identify known and unknown sources of force. Even if there were a hole at all, it would be a relatively small one, as you're comparing the amount of impulse required to turn a rocket around from 0.5c to -0.5c in a period of hours or weeks, to identifying subtle behaviors of systems... These are going to be orders upon orders of magnitudes of difference between the subtle forces that are "unknown" and the obvious rocket impulses that turn a rocket around and cause accelerations on the order of half the speed of light. Also, we can perfectly well do geometry without knowing every force that holds the paper together. We can be relatively assured that the space between points remains constant, unless someone wads or rips the paper. If there is an event that is sufficient to wad or rip the spacetime during the process of the twin paradox, I suspect, the traveling twin and the earthbound twin would probably notice. Subtle forces that are beneath notice, though, would barely affect the situation at all. The A-priori-ism is that "An inertial frame is not being acted on by any forces. PERIOD." It makes no difference whether they are known or unknown. A frame that is acted on by forces is not an inertial frame. A frame that is not acted on by forces is an inertial frame. That's not even a priori assumption That's is a theorem that results from a definition that says "POINTS DO NOT ACCELERATE". It does not matter how much force you apply to a point. It won't accelerate. If it is a "point-mass" it will accelerate. But if it is just a point, it won't.

A lot of strawman arguing in this video. I don't think the content creators referenced here would agree with these interpretations of what they were saying (I know I don't). A number of problematic issues arise with the statement "If we formulate the Twin Paradox in empty space..." at 7:51. This is unphysical and probably useless for this thought experiment. Would the space-time formed between the two objects even be Lorentzian? If not, SR can't be used here. But if using GR, then how would a destination (location and distance from origin) for the TT be determined? The later stuff about observations and deductions is just bogus. Nobody is arguing that the Twin Paradox is resolved as a function of the conscious observer. And last, the author gets overly fixated on defining inertial reference frames in purely realistic terms. Its well established that they are idealizations used for simplification of the thought experiment as occurring in flat Lorentzian space.

a person on earth isn’t really at rest compared to a rocket ship that flies away from it because isn’t the earth always moving around the sun at the same time also? and that sun with the planets also moving too?

I agree here that in essence the explanation really reduces down to the other one. It is not hard to show that all these perspectives and explanations are essentially equivalent. But, I believe you haven't fully grasped the meaning of the 'inertial frame switch'. You had shown in the first video a screenshot of the explanation from Schutz which I thought did a good job but essentially the crux is this. If we are to be talking about an observer, we ought to have a physical means of doing so. There is no physical way to travel such a path that instantly turns around. Mathematically, we require a differentiable timelike worldline to count as an 'observer'. This path is not differentiable at the critical point. As a result, we can not consider any physical coordinate description of that observer, because they aren't an observer in the first place. This is the solution to the problem so far as considering a physical paradox. However, this seems like a mere technicality and this gets into the 'inertial frame switch'. Moreover, in what respect can we not just consider the other frame? We may instead consider to physically accomplish the 'turn around' instead to have another spaceship to travel in the other direction when we meet, with synchronized clock settings at that point. Then, this gives an actual manner to accomplish what we want. But then it's clear that while this situation isn't the same as the other one (which, is seen to be aphysical), it does give in part an answer as to where that 'missing time goes', that of the skipping over when we switch to that other frame that has now different slice of simultaneity. Therefore, we are in essence asking to calculate in these coordinates, the time elapsed of a path that we don't even see fully. There is another well known instance where this happens-black holes. When one falls into a black hole, an outside observer will view it as taking infinite time, but the in falling observer will face in finite time. This is of course due to a result of our coordinates. With this understood, we see now why the 'turn around observer' should not be thought of as a frame but instead 'two frames'. In the accelerating case, it indeed should be thought of as a frame and I'll get a bit on the other video where that is addressed. It is not saying that the turn around observer is 'two inertial frames' but that the only operational way of describing the situation is by two inertial frames-our aphysical assumption about some impossible 'frame' is what leads us astray. As to the second half of the video... I must be must less sure. I have a few ways in which I think some things are wrong, but not myself any clear formulation. I prefer to come back to this question perhaps in the gravitational aspect that Einstein saw in the explanation, but having churned through some of my own research, find this question to be... very complex. However, here are a few things that come to mind- As to the conception of the 'inertial frame', as I mentioned in the past video, I find it highly unreasonable to 'remove the universe' and then ask 'whats the inertial frame'? Einstein's whole theory is based around the fact you can not separate the matter content, space-time coincidences out from space-time itself. Coordinates alone do not tell us the nature of our measurements, of the nature of forces, or dynamics. This is a well known aspect of relativity and certainly not one glossed over. For instance, in Newtonian dynamics, it is us on Earth that are essentially inertial and forces that act that cause free fall. However, in relativity, it is us that is in an 'accelerating frame' and those in free fall that are truly 'inertial' with no forces. This tells one that obviously the notion of an 'inertial frame' is fairly context dependent on our understanding of forces. This is naturally a point that is very complicated and I won't proclaim resolved. I will really need to think about it. It's in my perspective that the issue of 'what is an inertial frame' may be a red herring since in general relativity, there are no global inertial frames. As a result, it becomes only a local quantity. Laws of physics have to be formulated covariantly (I will right in the next video on exactly what this means since you mention it in there) Inertial frames simply arise as that which give the simple laws and follow along the natural path of inertia in space-time, independent to coordinate prescription that I believe to be trivially doable by linear algebra (the physics is in the formulation of the space-time in the first place, and objects as traveling on geodesics). It is thus us isolating out inertial frames and not the universe. Finally, I believe you mix up an epistemological question with an ontological one. It is us that decide how *anything* in physics works. Particles in free space simply abide by some rules that we try to ascribe. They don't have to 'know' if their frame is inertial-they don't need in fact coordinates in the first place. We use coordinates as a computationally convenient way to describe and label space-time. But if they were, they would need other physics information to computationally use. Here, this would be the metric, by which under our current theory of physics, would describe what forces they act under. Whether that is 'truly' happening under the hood is a question of ontology and science is always model based and we can never ever be sure whether anything in physics works the way it does we imagine.

What about this simple argument: Even though the situation is symmetrical if you think only moving back and forth, it is not symmetrical in one respect. Only the space twin resists the law of inertia whe he/she turns. There is something absolute in it even though you do not think how he/she does it. Even though you can think that the earth + the star move back and forth, they don't resist the law of inertia.

In my opinion the twin paradox can be examined without having to indicate that one of the twins turns around, switching inertial frame is not the solution and the acceleration also is not the solution. If one twin turns around, the other turns around and comes back too (I prefer to talk about the clock paradox), the astronaut twin can continue to travel with uniform rectilinear motion. (Why not?) In an empty space it's impossible to determine the solution but, if we know that one of the twins in the spaceship reaches a star, then the astronaut twin is certainly younger than Earth. (The Earth and the star belong to the Earth's frame and, obviously , the other twin must remain on Earth). If we don't have this information, Emmy's frame may also be younger than Albert's frame. (even "spaceship Earth" can travel while Albert is at rest), THE SOLUTION OF THE TWIN PARADOX IS INDETERMINATE!

I do agree that the other videos don’t give the correct solution to the twins’ paradox, but unfortunately I’m also not convinced by your arguments. You keep saying that acceleration is only a relative property defined through coordinates, but this is far from truth. The true spacetime acceleration vector is defined as the covariant derivative of the spacetime velocity vector in the direction of itself. This acceleration vector would be relative if the spacetime velocity vector is also defined in a relative way, but it’s not. The spacetime velocity is defined as the vector field whose vectors at each point are tangent to a curve in spacetime. If this curve is being traced by a real object (like a spaceship) then the curve is also a “real object” and hence should not change under coordinate transformations. Think about this like parallels and meridians on earth. Those imaginary lines define a coordinate system and as such they are arbitrary, but a plane taking a great circle path from London to New York won’t suddenly change its path if you redefine the coordinate system; it remains the same. So this means that the spacetime velocity is also real and invariant under coordinate transformations and hence the same goes for the spacetime acceleration. I think your confusion stems from thinking about the components of the acceleration (which are indeed relative) but not the vector itself. Physically, the accelerating twin would distinguish that they are accelerating by having an accelerometer with them, and that accelerometer would output a number different from zero, and this number remains the same no matter the coordinate systems from which the twins are looking at it.

I starded studying special relativity on my own, i don t get what s the problem or maybe i did not understand sr. From what i know in sr an inertial frame is one where all worldlines of a photons move on a straight line. Sr is based on the fact that light speed has to be the same in all of these frames and that the laws of physics are the same. By only assuming these two principles you can prove that two such frames are related by Lorentz transformation, and by using these transformation you can prove time dilation. In this video, by using the definition i know of inertial frame, both A and B cannot see worldlines of photons as straight, at least one of them has to be non inertial. The thing you cannot deduce is that the proper time of B is the sum of the proper times of his motions during the two situations i.e. proper time depends only on instant velocity and not acceleration. I think that the formula of proper time for accelerating particles is taken as an axiom, but it does not create paradoxes. Tell me if i got something wrong, i want to learn this subject.

You are talking about coordinate acceleration, the accelarion to take into account is the covariant acceleration (en.wikipedia.org/wiki/Acceleration_(differential_geometr)), it's norm is coordinate independent . The twin on the spaceship is subjected to a proper acceleration ( during the "switch of the inertial frames") the earth twin no. The Christoffel symbols are not zero during the switching of the inertial frame, that is the cause of a gravitational force in the spaceship reference frame (curvature is zero but for the equivalence principle we can consider the force gravity) and the earth proper acceleration in the reference frame of the spaceship is calculated as a_earth = a_coordinate + gravity = 0, so earth does not accelerate while the a_ship = gravity = ship_propulsion that is not zero . To do some more rigorous calculus one could use the rindler coordinates (the coordinates of a reference system that is subjected to a constant proper acceleration) . The law of physics are valid in all reference systems (accelerated, rotating, polar coordinaes, ecc), an inertial frame is only a reference frame in which they can be wrote in a simpler way( for example the Christoffel symbols are zero in general in an inertial reference frame). If there are forces that are not four-vector and with a change of coordinates they disappear probably are fictious forces do to the coordinates chosen. ps. Sorry for the english.

If "feeling the force" allows one twin to instantly age more than the other, does this not imply faster than light cause and effect?

Here is a fact: if I know which of the twins is in actually motion relative to the other twin, I will know whose clock runs slower. This is also true if I am one of the twins. Now, as one of the twins I usually can't know this unless I experience acceleration or am able to compare our positions to some landmark. One landmark that should work in this scenario is the cosmic background radiation, I can have a pretty good idea who is in motion by comparing our positions to the CBR. Now, if I didn't have that advantage, I would need something like acceleration by one of us to see who was actually in relative motion. This kind of relates to the idea in this video of using force to identify the person who is accelerating, except that I am denying that acceleration is necessary. I think it is sufficient but not necessary--at least in principle.

Just wrong. Acceleration is a Lorentz scalar, a^\mu a_\mu=\alpha^2. A worldline is geodesic or it isn't. The TP considers the worldline arc lengths of two travelers, \Delta \tau=\int_\gamma d\lambda \sqrt{g_{\mu u}\dot{\xi}^\mu \dot{\xi}^ u}, between a pair of events. Time dilation is something else, the projection of the tangent vector to the traveler worldline onto a set of arbitrary basis vectors we identify with the "observer."

Maybe that by conservation of momentum any force that a twin feels must be generated by the acceleration of a source? Like in the case of the rockets you get a new frame when you fire the rockets (The exhaust gases frames) and with 3 frames maybe you can resolve the paradox?

The acceleration could be a tiny part of the journey once the spaceship was up to speed it could coast so why would they age less on that part of the flight?

I don't agree with what you say at 4:55 about the fact that situation stays symmetric if we assume that twin B is in rest. In this case from B's perspective, at the beginning, twin A would move away being being behind him, then travel a huge semicircle to appear in front of him and then come back. This is not at all symmetric to the situation if A is in rest

The real paradox was the twins we met along the way

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

Instruments allow you to measure accelerations in every point of your frame if forces exist, while if they are ficticious or product of a coordinate change, then your instruments won't measure them. So it seems to me we still can observe forces/fields that way objectively.

If the travelling twin decides to think from the perspective of earth twin, does he make some enormous scientific error? He accepts that he is the one who is moving, makes calculations that his own time is slower and so on. Can he do some experiment there in the space (alone or co-operating), which contradicts his 'new' thinking?