Solutions to the Twin Paradox are STILL Wrong
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- Опубліковано 14 тра 2020
- Are "solutions" to the twin paradox STILL leaving you confused and skeptical? In our follow-up to "Why Solutions to the Twin Paradox are Wrong" we dive deeper into popular UA-cam videos, examining spacetime diagrams, the Lorentz Transformations, and other tools that are often incorrectly used to resolve the paradox.
Feel free to leave any questions or thoughts in the comments below!
Full Twin Paradox Playlist:
• The Twin Paradox
Link to "Why Solutions to the Twin Paradox are Wrong":
• Why Solutions to the T...
Link to "Can You Feel Force?"
• Can You Feel Force?
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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 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.
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.
Yeah but relativity doesn’t tell you anything about how to define “inertial” - and from classical mechanics it’s defined via acceleration. So there’s a terrible circularity issue
@@WSFeuer Of course it is defined by accelleration. But there is nothing circular about it.
You have to understand that when you have one inertial frame, than ONLY frames that can be created by lorentz transformation are also inertial.
And accelleration is measurable locally. What the video says about this is just wrong... E.g. only in an inertial frame the laws of physics don't depend on orientation. Let's say you start with a body moving in x-direction. In an inertial frame it keeps moving in x-direction. And if you start with a body moving in y-direction, it keeps going in y-direction.
Now do the same in a reference frame that accellerates in the x-direction. The first body (starting in x-direction) would accellerate but move straight, the second one (starting in y-direction) would move on a parabola.
And to make it clear: a reference frame is a construction that lets you pick numbers for position, velocity, accelleration etc. Of course you can pick frames in a way that accelleration can be any number you wish. But this is NOT the physical accelleration, which can be calculated in every frame you wish and is always the same... as it should, because it is PHYSICAL, and not just a parameter reference.
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.
What I think the maker of the video is correct about is that you need your problem to be well defined in order to solve it.
Most people who formulate the twin paradox have an implicit assumption that there is a clear inertial frame of reference. You do need that in order for this to be well defined. This is easy enough to do. Both twins have clocks right, so when they initially set their clocks on earth you define that as 0 acceleration and away one of them goes. Then acceleration clearly breaks the symmetry and it's well defined.
Most people don't have a problem with this because they implicitly assume the guy on earth isn't going to be zooming away and then changing inertial frames and zooming back.
The guy who makes this video though won't stand for that. He asserts as a condition of the problem that you can't identify an inertial frame. That's the equivalent of trying to solve the twin paradox with the twins starting on opposite sides of the universe out of causal contact though. It's not realistically solvable by GR or SR. They wouldn't even be able to synchronize clocks in that case. It's not a well defined problem.
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.
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.
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.
I believe that at this point, the video poster merely wants to point out that the mere kinematic definition of acceleration (i.e. change of velocity) is not sufficient to resolve the ambiguity of who is actually changing the reference frame. As you said, "feeling the force" is an actual indicator of a change of frame.
@@NeedsEvidence I appreciate the reply, but if that is all he is pointing out, then it does not seem to present a legitimate argument for invalidating the traditional solution to the twin paradox, at least as it pertains to the special relativity version. I mean in practical terms there is no ambiguity at all as to which twin was exposed to an accelerated reference frame, and how we can correlate that to their younger age upon their return.
@@MrBendybruce Maybe the video poster is overdramatizing the problem (haven't seen his follow-up video as yet so I can't tell if there is something more to it).
Having said that, the problem of identifying whether you are in a non-'accelerated' (inertial) or an 'accelerated' (non-inertial) frame of reference is actually not trivial. It has eventually been resolved by General Relativity. However, one doesn't need to invoke that to solve the twin paradox.
If a freely floating body detached from an observer (e.g. the traveling twin) is first at rest with her but then suddenly starts moving relative to the observer without forces acting on it (thus violating F=ma, which is valid only in an inertial frame), then this objectively indicates that the observer has changed the frame of reference (has objectively accelerated). That's all there is to it.
@@NeedsEvidence You said "without forces acting on it" but Dialect claims that feeling force isn't a valid argument. So how can you prove that these forces are not fictitious?
@@-_Nuke_- what does claiming that feeling a force isn't valid even mean? If you are in an accelerated reference frame, you feel a force whether it is in a rocket ship or standing here on earth. In the twin paradox that focuses on special relativity, one of those twins is in an inertial frame and feels no force. The other twin who is in an accelerated reference frame does feel a force. There is no ambiguity here as to which twin is accelerating and which one is not. That's the point of my question, because dialect suggests either twin can be said to be accelerating and I don't see how this claim can be supported when only one twin feels the force.
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.
Indeed, when you look into it, you discover that "real acceleration" (due to forces) is defined as acceleration relative to an inertial frame. So it is a kinematical 3-acceleration that is made in an inertial frame. So long as you know your frame is inertial, this definition is unproblematic. But how does one know one's own frame is inertial, especially since the inertial-ness of frames are defined via acceleration? It's a viciously circular definition. We follow this topic up most poignantly perhaps in Newton vs. Mach (and will be returning to it again quite soon in new videos!)
@@dialectphilosophy So, that means that, *the outcome* of the firing of the engines of the spaceship is relative?
If yes, then that means that we can have a scenario - where we can logically explain - how the Earth - a huge spherical and rigid body, with no obvious mechanisms of acceleration whatsoever - can somehow accelerate close to the speed of light and then turn back (?) and meet us in empty space?
What about the amount of energy that the spaceship and the Earth both spend (each one by themselves) in order to accelerate?
So purely speaking about quantities of energy being spend, can't agree that this breaks the symmetry?
I mean, I can't think of any scenario that logically speaking, the Earth can do the motion that you described... How can a planet undergo such motion?
How can the Earth find such tremendous amounts of fuel to accelerate to such speeds? (I assume that since the spaceship is capable of doing that, it should have all the means to do it, but the Earth certainly doesn’t.)
Inside the spaceship’s cockpit, we find the "hands on throttle and stick" controls that control the acceleration of the spaceship in multiple directions. If we change the scenario, then that means that these same controls can change the acceleration of the Earth!? And do that instantly as well?
Imagine the spaceship twin, in the second diagram (the one where the spaceship stays and the Earth undergoes acceleration and then turns back (4:33)) - not just sitting there being inertial, but also - being able to control the motion of the Earth INSTANTENIOUSLY from his cockpit...? How?
I don't get it, what am I missing
@NUKE on a roller-coaster ride, you are constantly being accelerated and decelerated and changing directions. As a passenger, are you aging more or less at each in direction/velocity. Or are you just along for the ride and are essentially in a state of rest?
If you take a sensory deprived ride - deaf and blind - you hardly know that you are in motion. The aging process is undergone by the cars themselves as they are jostled around on the track. You, as a passenger, return as though you had never gone on the ride. At most, you would be slightly older due to the slight amount of additional force applied during the ride that wasn't absorbed by the rail car.
@@-_Nuke_- Think of it this way... the rocket here is using propulsion to combat the earth acceleration that has been pulling it.
Is like if you were on a moving train and you move backwards in such a way that the train speed combined with your speed is now equal to zero to the rails.
Kinda like being on a treadmill were you are clearly running but due to the treadmill movement all you do is now nullified.
In the train example my legs walking backwards do not have the strength to move the whole train but still if I was to mark my point of view with the ground I am not moving, only because I am applying the same acceleration the train has to myself.
Or in the treadmill the tread is clearly moving and it can even keep accelerating but I myself who is running on it can also accelerate and keep myself still
@@dialectphilosophy How do we know? By the experience of inertial forces during the acceleration, surely.
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.
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?
No, because you can run the experiment without acceleration and still get one twin that is younger. There are two points to this thought experiment, the first is what causes the actual time dilation, the second is why does that only happen to one twin, what is the difference between them both.
If we simplify the experiment and remove acceleration. Have the twin B already travelling at 0.8c towards the star as he passes twin A who is stationary. The star is 10ly ( light years) distance. When B passes A he starts his clock and instantaeously A starts his. Lets also start at the same time a clock on the star, so we have clocks A, B and C.
When the Twin with Clock B arrives at the star, still travelling unformally at 0.8c, he stops his clock, which instantaeously stops the other two in our thought experiment. That is the experiment finished, all the clocks can now be collected up at leisure after a few pints at the pub and compared, or if you a "God" simply note the times.
Using the Lorentz transformations for the 10 light year trip both clock A for the stationary twin and clock C for the stars clock shows 12.5 years have passed. Clock B that travelled to the star shows 7.5 years. So less time has passed. The twin has not aged as quick. Only constant velocities have occured during the actual experiment, no accelation or turning around.
This is not very surprising because it matches what we see in real situations such as cosmic rays and fast moving particles in particle colliders. The moving particles age less than "twin" particles at rest before they decay etc. Special relativity is about uniform velocities after all.
The 2nd question, what is it between the two Twins then that makes a difference on who has time dilation ? Einsteins' rules say one reference point does not have priority other the other for uniform moving bodies. Neither of the twins can tell who is moving. From Twins B perspective Twin A has moved away 10 ly and the planet has moved towards him 10ly; he has been stationary relative to both.
From all the youtube videos the "difference" has been assigned a lot of different explanations. Some from professors etc and they are on varying levels of complexity, I MUST COMMEND EVERYONE WHO DOES THIS AS IT IS QUITE BRAVE ... considering the comments sections !
In my experiment above no acceleration happens and as mentioned in real life there is no paradox either. So what is the difference? In my example you can see what makes the differeence if you gives the A, B and C clocks co-ordinates in this world (space / spacetime / universe etc) such as x, y, z. So we might have 1,1,1,T1 and 2,2,2,T2 and 3,3,3, T3 .
The difference is that only Twin B actually changes his universal co-ordinates during the experiment. Changing co-ordinates implies directly a distance moved of course and this implies a velocity which gives the time dilation. Note that the direction is not important.
As an interesting aside if Twin B noted that his clock has progressed 7.5 years when he arrived at the star he would have been able to determine that it was he who was moving towards the star and not the star towards him. If the star was moving towards him then to have travelled 10 ly in 7.5 years means it would have had to been travelling faster than light. Using the equations he can work out he was actually moving, having done a distance of 6ly in 7.5 years so having travelled at 0.8c velocity. Distance shortens as well of course for the moving body.
@@zakelwe Exactly. Your last point is an interesting one, and seems to suggest, again, that the two frames are not equivalent. Distance contraction occurs for the traveller, not the static observer. This looks to me like another way of seeing the asymmetry being assumed, and I am not at all sure how this might be explained by the relativist. Needs more thinking!
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).
I'm curious how you would explain GPS satellite time dilation if acceleration is the only solution to the problem. Is the difference in gravity field the only influence on dilation in that case? Acceleration seems like a red herring when the time at different velocities seems to be the important contribution of the difference in age. But maybe I haven't thought this through enough.
@@dilutioncreation1317Most of the disparity in GPS clocks is due to gravitational time dilation. What little disparity there is as a result of SR is tiny since relativity of simultaneity is proportional to the relative speed and distance of an object. Since satellites are quite close to earth and are only travelling a very small fraction of a percent the speed of light relative to us, relativity of simultaneity is miniscule. Also, relativity of simultaneity affects event disparity in the direction of relative velocity. Satellites are, for the most part, neither moving closer not further away, so that presents is effects even further. And finally, satellites travel in an ellipse, which means they switch between going towards us and away from us constantly, which just cancels out relativity of simultaneity even more.
@@GoofyAhOklahoma I don't think it cancels out since it would be the same as the original twin paradox
It's incorrect. Acceleration is in fact absolute.. it's equivalent to gravity, meaning that, just like the metric tensor, it's local.
agreed
This guy is ignoring the definition of acceleration. F=m.a has it's own relativistic version of course (a lot of them actually). The most intuitive one is T^{ab};_b=0 , T being the energy momentum tensor. You can't "make up" an acceleration. It's there because there's an agent exerting a force on an object.. the "fake" acceleration that appears when switching coordinates is equivalent to "fake" forces like Coriolis for example.
Doing that little change has no consequences in SR, but it has serious consequences in GR, because any agent will appear in the T tensor and create more gravity locally.
Emmy is not truly in a uniform gravitational field. There will be a small but non-zero tidal force that allows us to determine whether she’s accelerating or not. Albert actually accelerates and therefore does not experience a differential tidal force. Though the effects are small, in principle they allow us to determine who has accelerated and who has not.
@@randomdude5649 Yes it does solve the problem. I couldn't understand a single thing about what you just wrote to be honest. But I'll say it again: special relativy is more than just Lorentz transformations: the definition of acceleration is still local, since it involves an energy momentum tensor on the manifold.
This is what I thought also
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.
The very nature of this paradox is that we do not know which one of them is moving or moving faster. The one that is moving with or without acceleration compared to the one that is stationary will experience less time. If only two of them in space-time alone the only reference of any movement is one of the two if we think space itself is nothingness. We only know they two move in different speed but can never determine which one is moving or moving faster unless there is an inertia system independent from them two. The fact that two of them age differently does prove that one of them is moving faster relative to an inertia system that is other than them two. What is that system then? It's the stationary ether
@@519stream3 this is just wrong. What we know is that one twin is always in a single inertial frame, the other twin is in two, at different times. Once you understand that, the twin paradox is no longer a paradox.
@@simonwatson2399 well you might be right about this. Actually the destination is always stationary to one of the twins but it is moving relative to the other which I think does break the symmetry. The distance between the starting point and destination point are not the same to the twins. But I still believe the now we call space-time is eather itself or it can not be bent unless it is a thing. Its existence is not an option and it permeates everywhere and bonds to all things that exist. And it moves at speed of light at all time.
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.
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
Exactly. He makes an ideal model of acceleration, where one could change speed, i.e. accelerate, all at once. That's why he can claim that acceleration is not felt. From this he posits a symmetry. But acceleration is never universally applied; ship have to change speed, and Bob inside the ship feels this change in speed as illusory force that pushes him back on the seat. His explanation also presupposes a ideal Newtonian homogeneous space, not relativistic space-time. Also completely ignores length contraction.
But in the end of the day, it's good to see some debate. It can only strengthen our collective understanding.
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...
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.
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 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.
I just wanted to write the same!
That’s just not the case. If there is an independent inertial frame, it would just see Albert and Emmy going into different directions faster and faster, until accelerating into each other again.
Besides, if there is a universal frame for accelerated movement, then what stops the universal frame for inertial movement to exist as well?
I mean think about it. The only difference between both is that one changes over time.
@@user_null3696 That is not true. the independent inertial frame would clearly distinguish which one changed the direction of motion. The inertial observer would see only one of them accelerating into the other one. It is easy to do this thought experiment in your head.
"if there is a universal frame for accelerated movement, then what stops the universal frame for inertial movement to exist as well?
I mean think about it. The only difference between both is that one changes over time."
Well, the global frame for accelerating observers is the one that is not accelerating but it won't tell you anything about inertial frames because you don't know the initial velocity at which it started accelerating because the initial condition for an accelerating frame is velocity but it is relative.
The global accelerating frame has the freedom in choosing initial conditions which is velocity. So therefore for every single accelerating frame, you have infinitely many corresponding inertial frames and therefore there are infinitely many inertial frames for global non accelerating frame.
@@lukasrafajpps Well that’s one way to stretch out a phrase “no it won’t”.
But you are right. Since the distance between two inertial objects will change a certain amount per second, while the amount of distance changing per second between inertial and accelerating objects will keep getting bigger. So, once accelerated speed of second object will become faster than speed of third and first objects drifting apart, it will start moving away from the third faster than the first will from the third. (the opposite effect will occur if the second object decelerates)
However, what makes us know which frames are inertial and which are not? We could just as easily conclude that the second object is inertial, and the other two accelerate away at the same rate.
Is it that in order to accelerate a force needs to be applied to an object? In that case, what makes us know which objects has force applied on it? For example, for a planet the rocket accelerates away due to its engine, but from the rocket’ POV it’s engine is making the planet accelerate away.
But what really bugs me is a simple logical fallacy. Let’s say a rocket leaves a planet, and we assume that acceleration is absolute. From rocket’s POV the planet accelerates away, but it doesn’t matter, because we know for sure that it is indeed rocket moving away, and our planet stays stationary. Acceleration stops, and the now inertial rocket therefore can be related to the planet. Therefore, from rocket’s POV, it moved, but then just immediately stopped, with the planet suddenly just deciding to start moving with the achieved speed instead. Not only did the stationary planet change speed WITHOUT acceleration, but also achieved the speed of SOMETHING ELSE’S acceleration. One thing accelerates, but then another starts moving.
Not to mention the fact that, if only inertial frames are relative, and pretty much everything accelerates and decelerates all the time, then that means that relativity cannot be applied to pretty much anything in any shape or form.
I’d really like to hear your opinion on this.
@@user_null3696 "Is it that in order to accelerate a force needs to be applied to an object? In that case, what makes us know which objects has force applied on it? For example, for a planet the rocket accelerates away due to its engine, but from the rocket’ POV it’s engine is making the planet accelerate away."
Well, in inertial frame if you put an object on some place, it would stay there. If you are in non inertial frame, then the object would move. You might ask, what about space station? It is in a gravitational field therefore the force is applied on in which makes it to orbit around the Earth. This system is so called locally inertial frame which is exactly the way Einstein generalised the special relativity on accelerating frames called general relativity. It says that you can't distinguish locally whether you are in free fall or not and therefore special relativity apply but if you want to transform coordinates into a different point you have to use non trivial metric to do it.
"But what really bugs me is a simple logical fallacy. Let’s say a rocket leaves a planet, and we assume that acceleration is absolute. From rocket’s POV the planet accelerates away, but it doesn’t matter, because we know for sure that it is indeed rocket moving away, and our planet stays stationary. Acceleration stops, and the now inertial rocket therefore can be related to the planet. Therefore, from rocket’s POV, it moved, but then just immediately stopped, with the planet suddenly just deciding to start moving with the achieved speed instead. Not only did the stationary planet change speed WITHOUT acceleration, but also achieved the speed of SOMETHING ELSE’S acceleration. One thing accelerates, but then another starts moving."
The velocity of the planet is changing only relative to the non inertial observer. There is nothing wrong with it. For the observer on the spaceshit the whole universe accelerate but the whole universe would agree that it is in fact the rocket accelerating. The stacionary planet remained stationary no matter what the guy inside the rocket did because again it did not changed its velocity relative to any inertial frame in the universe.
I think this is very unnecesary complication you are talking about and actually if it really was a problem, then it is not only a problem of Einstein relativity but Galileo's relativity as well.
"Not to mention the fact that, if only inertial frames are relative, and pretty much everything accelerates and decelerates all the time, then that means that relativity cannot be applied to pretty much anything in any shape or form."
That is true. There is in fact not any purely inertial frame in the universe but there are as I already mentioned locally inertial frames. What it means? It means that if you are let's say in a uniform gravitational field, there would not be any possible experiment to tell that you are in such a gravitational field because everything around you would experience the same acceleration. This is why we are talking about locally inertial frames because usually on big scales you can distinguish this but on infinitesimally small area you can't.
You are right though that special relativity can never be applied 100% in real life but if you are in some interplanetary space it is an extremely good approximation of an inertial frame not to mention an interstellar space. It is just an effective theory and you need to properly underestand its limits to use it otherwise you must use the general relativity which applies everywhere in the universe except singularities inside blackholes.
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.
We've seen it. While we're glad she makes many good points about misunderstandings in relativity (especially how gravity is not a force) she makes the same error in reasoning as other physicists in asserting that "acceleration is absolute" because "we can measure it." Indeed, she has not thought out her theory of measurement very deeply, because what a measurement of acceleration truly is, is a measurement of acceleration relative to an inertial frame -- but no empirical measurement can tell you whether your frame of reference is inertial to begin with. It is generally assumed a-priori from the context -- see our video Newton vs. Mach for more on this subject.
Sabine had so many jokes in the latest video that Im not sure if she really meant acceleration is absolute.
@@dialectphilosophy her rationale for claiming that acceleration is absolute is that a spring can tell you if you are accelerating or not. Is that not an accurate statement?
Acceleration is absolute. You can absolutely measure acceleration. It's the thing that kills you when you hit a brick wall at 100mph. When there are no forces acting on you to cause acceleration, you would be weightless. If a rocket with you in it accelerated at 100g, you would die. Seems pretty absolute to me.
Thinking of spacetime diagram. We dont need to know the forces or prime movers that set up velocity for the rigid bodies for different frames. Why suddenly we would need a force to precursor acceleration in the diagram? The plain diagram can be used to present acceleration in a curved line. And that same line can be easily shown to be a straight line relative to other rotating frame on a specific way. Acceleration in euclidean spacetime is relative, and satisfyingly so. Whether they measure, feel, or dont feel acceleration or any physical property whatsoever, should have nothing to do with the special relativity math. And even less has the acceleration prefered status on the general relativity by the general coordinate covariance principle.
No acceleration is not coordinative. Proper acceleration is a scalar all observers agree on.
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?
No, then you will need a third observer who is inertial...who can correctly apply the time dilation formula.
Ignoring the spaceship altogether, yes they would be the same age when they reunite, and there’s no paradox because they traveled essentially the same spacetime path, so the arc length of said path is the same for both, and proper time is defined through arc length, hence they measure the same time passing for both.
Yes, you had it pretty much right. So long as they travel like-for-like in opposite directions then it doesn't matter how they move or where they go, there will be no discrepancies in the twins relative motions. And, as they both witness the same time dilation and length contraction, neither will record any discrepancy in the spacetime durations for their journey. Whether or not this would remain the fact should they become causally disconnected from each other I'm not sure, better ask a physicist!
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.
The real key to show there is no paradox is Rlativity of Simultaneity.
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 do realize that in this test you say the spring effect is being perceived relative to the weight right?
@@walls171 Pretty long comment, but I guarantee it's worth it: Stand in your room. Hold a slinky or a string. Take a step to the left and observe what the slinky does. You moving to the left requires acceleration to the left. The slinky, relative to you, moves to the right for a beief moment. From the slinkys perspective, you are moving to the left for a brief moment. This same experiment also works on a train, and in every inertial frame of reference, because physics in any inertial frame of reference are the same. Now apply the same experiment back to the twin paradox, where each twin is holding a spring. Assume the twin in the ship travels right. If the twins want to meet again, one has to accelerate. The space twin would need to accelerate to the left. In that case, their spring would move to the right. If the earth twin were to accelerate, they need to accelerate to the right. Their spring would move to the left. But here is the whole crux of this thing: When you say acceleration is relative, you are saying the springs change behaviour, depending on your reference frame. You are suggesting that the space twin sees the the earth twins spring move to the left, while the earth twin sees space twins spring move to the right. Assume a third frame of reference, that travels half the speed of the space twin, thus it is always in the middle of earth and space twin. You are suggesting this third reference frame sees earths spring move to the left, and spaces string to the right, both at the same time. This is bogus. No space contraction or time dilation can explain this. Either the spring moves, or it does not. Acceleration has to be absolute.
@@rismosch You failed fast, to stablish a direction from which I would move I will need to first stablish the point of departure, also if I move and expect the slinky to be dragged behind then it was me accelerating in relation to the slinky which wasn't as the slinky didn't change direction with me rather was dragged.
@@walls171 Come on man, really? Now you are just dishonest. Obviously, moving in a direction is only relative to something else. Discrediting the whole argument on an assumed technicality is simply dishonest. To actually counter my argument, you need to do this: Explain why the space twin would see their spring not move (relative to themself), while the earths twin sees the space twins spring move (relative to the space twin).
@@rismosch again the big issue in your explanation is that you are dragging the slinky in how you explain it meaning that the movement was more like you accelerated in relation to the slinky and then you pulled it.
There is actually a watchable and playable example of how relativity actually works if you want to visualize it better.
A game called outer wilds I recommend it bc it really does make you see it and feel it how relativity does work
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.
yeah, that was my first thought. If they were to accelerate and move at the same rate at any given point in space and time, they would see each other in same referential frame, and so they would meet each other with the same age. This is a bit confusing to me.
that’s exactly what i was thinking!
In that case yes they would be the same age, since their relative motion according to the initial reference it is exactly the same. If one of them accelerated faster than the other, and therefore their speed would be higher, that one would be the younger.
@@mrboombastic8369 That's right. You got the point.
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?
@@silverrahul yea i just realized the v is squared in the Lorentz equations. Sorry for the stupid question
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?
One twin would literally age slower w.r.t. the other twin. Particle decays (and biological processes etc.) would also slow down w.r.t. the resting frame. But keep in mind that for the traveler, everything would age normally as usual. It's just that less time passes for her.
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).
Your explanation makes sense to me. Why is there such disagreement among physics videos, makes me doubt what I watch on UA-cam now.
@@SpontaneityJD I've watched a few other videos from this channel. What appears to me is that he is just trying to make a point because the other videos are not precise enough, from his own point of view, but he's actually not saying anything different.
What he claims is that one should not confuse acceleration and the actions of external forces, but this distinction is misleading as Newton's second law is taken as a definition of acceleration in the whole scientific literature. The consequence of that is that acceleration ceases to be the derivative of speed in special relativity outside of inertial frames of reference, so his definition is in contradiction with literature but it actually embeds the same physics.
Basically, he's arguing for the sake of arguing and with his own definitions on top of that, which is not good science popularization imho.
For popularizing the idea, the best material is, in my opinion the spacetime diagrams as shown in minute physics videos. They are very visual stuff, relatively easy to understand, yet completely accurate. In a physics lesson, one would explain that such a diagram can be used only in an inertial frame of reference and that it's not the case of the traveler's frame of reference as he is submitted to external forces (which is a given of the problem). But this are the kind of precisions you would give in a lesson on the topic not necessarily on a UA-cam show. At least, omitting this doesn't make you wrong, at worst inaccurate.
That said, there is still quality material on this channel. In particular, he proves the idea that gravity is caused by time dilation to be wrong, I do recommend this video. And yes, I'm very much aware this means the channels I was defending the paragraph above are now wrong and he's right on the topic, but it's not my fault! 😅 Actually, even great channels such as PBS spacetime make mistakes on regular basis, even sometimes the whole point of the video is wrong (for instance, all videos about what's going on in the interior of a black hole are pretty much bullsh*t...). That's the problem with science, it's difficult and popularizing supposes some very deep understanding because you can not even rely on the math as teachers do.
I hope it doesn't discourage you to watch scientific content but on the contrary try to get deeper into it!
@@fuxpremier Great insight, thank you. What if I told you, you also read my mind. I was about to ask you your thoughts on time dilation causing gravity (an idea which I found myself to be naturally repulsed to). Glad to hear you agree with his debunking of that convoluted idea.
You have a very sober perspective on these topics in general; perhaps you should start a channel haha
@@SpontaneityJD Ah ah! Making quality videos requires skills that I don't have, but I'm always happy to discuss physics! Thx for your kind words anyway 🙂
@@fuxpremier Well, since you're here... I've recently watched one of his videos on the notion of gravity. Specifically, that we (and all objects) are not falling down, but rather, that the earth is "falling" up.
This idea is completely new to me. Is it generally accepted physics? Also, I am still having significant difficulty reconciling this theory with the natural inference that the Earth cannot clearly "accelerate upwards" in all directions -- or the Earth would be increasing in size exponentially.
Any insight on this? Thanks :)
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.
Acceleration is any speed over 0. Cruising at 60 mph is still considered acceleration from 0 mph. Since everything is in motion, your measured speed is always going to be relative speed. To take a measurement that everyone else can duplicate, you establish a constant. That constant is currently the rotational speed of the planet.
An absolute constant is the speed of light as nothing can go faster. In space, you can measure your speed against the speed of light. Traveling in space, any change in the frequency/wavelength do to red/blue shift can be computed to determine how much faster/slower you are traveling.
Also, since atomic clocks are very precise, and the restoring force is constant, synchronized clocks will measure relative motion. This can be used to determine which object is moving faster than the other.
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?
@dialect What’s your response to the top comment which argues that the accelerating ship can be distinguished by dropping apples in each?
The apple can only accelerate relative to the observer that is measuring it. Thus, what the observer in the spaceship that is "firing its rockets" is actually measuring is a coordinative 3-acceleration of the apple relative to themselves. This measurement, being strictly coordinative, cannot in-itself signal the asymmetry. In order to indicate such, the 3-acceleration has to be somehow coordinated to an absolute acceleration (a 4-acceleration, or equivalently, an acceleration relative to an inertial frame). What allows an observer to make that logical leap is not included in the framework of special relativity (where the inertial frames are given apriori and not deduced empirically). This renders the twin paradox still paradoxical.
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.
If you accept acceleration is absolute, you must reject relativity, because absolute acceleration requires absolute space and time. See our video "Why the Theory of Relativity Doesn't Add Up."
@@dialectphilosophy In the context of special relativity, acceleration is absolute. However, this does not imply that it requires absolute space and time, special relativity combines space and time into a four-dimensional spacetime, which is relative and depends on the observer. One of the fundamental postulates of special relativity is that the laws of physics are the same in all inertial frames, which implies the relativity of space and time. Acceleration does NOT require absolute space and time in special relativity as Einstein himself postulated. Which shows you know absolute (no pum intended) nothing what you are talking about. Only in the context of GENERAL relativity all motion is relative and acceleration is no longer considered absolute. What is your educational background ?
@@hugo-garcia What is the meaning of acceleration if it can be absolute without absolute space?
I mean, Dialect's point is very simple. Acceleration is coordinative, it is just defined as the time derivative of a velocity vector. And, because it is essentially coordinative, it is relative to whatever coordinate system is being used.
To say it is absolute is to posit a privileged coordinate system, which is to posit absolute space.
@@2tehnik He is wrong because he is lying about special relativity. His arguments it are actually straw man falacies. In other words the assumptions he says special relativity proposes are not true
@@hugo-garcia You are not actually addressing the point being made.
The definition of acceleration in STR isn't especially different. It isn't suddenly a non-coordinative thing.
If you think that in some way that's false, I'm all ears.
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.
I agree !
No Simon. ACCELERATION in GR is relative because of the equivalence principle. If you want more clarification,let me know. I really hate writing pages here
@@nadirceliloglu7623 the equivalence principle doesn't apply to acceleration. That's basic relativity. It's possible to perform an experiment to determine if you are accelerating or not. If you don't get that, everything else you state is going to be wrong.
@@simonwatson2399 what?? Seriously?
Simon you are denying General Relativity! Are you aware of it?
Einstein would be furious to hear this argument.
You can NOT distinguish between acceleration and gravity locally whatever experiment is done!
This is the principle of General Relativity.
@@simonwatson2399 Either way, Special Relativity doesn't account for acceleration. So saying that any asymmetry in time dilation is predicted by Special Relativity (as many do) would be false. SR equations have no parameter representing acceleration.
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.
1) The one who fires his rockets can CLAIM that he is firing his rockets, BECAUSE he wants to stay at the same distance from the other due to both being inside a gravitational field...
2) And the one who isnt firing its rockets can claim just that, that its not firing its rockets, and the one who does - is the one that accelerates.
BOTH twins can find excuses to why they are not accelerating.
Acceleration -REQUIRES- *DEMANDS* an absolute frame of reference in order for it to be ABSOLUTE. And if we do have absolute acceleration then that *NECESSITATES* that such absolute frame really does exist.
So what is it? Do we live in a Universe with an absolute acceleration and thus a Universe with an global and absolute frame of reference?
Or do we live in a Universe where even acceleration is relative and thus space and time are also relative?
Let me remind you that NO MATTER if you are accelerating or not - YOU WILL STILL MEASURE THE SPEED OF LIGHT TO BE THE *C* NO MATTER WHAT YOU DO!
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.
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.
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.
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?
It's tempting to think that -- but then we must ask how is momentum itself defined? That requires knowing velocity, meaning we must know whether our frame is accelerating or not. You can see such a definition is quite circular.
Which formula is used in 11:06?
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.
@Paras Sharma Well I don't know your level so it's difficult to make specific recommendations. My favorite SR book is Special Relativity in General Frames by Gourgoulhon, but it's graduate level and so quite advanced and not really suited for a first studying, more like a reference. But if you're advanced mathematically you might try it. On an introductory level Spacetime Physics by Taylor&Wheeler is a classic choice. Honestly though there are hundreds of books on SR and most should be fine. It's all about finding a book that suits your style. However I would avoid most "Modern Physics" or "University Physics"-type books
I would also say most introductory General Relativity books contain good (but short) discussions on SR, they are more likely to emphasize the geometric viewpoint since that is essential for GR. The books A First Course in General Relativity by Schutz and Spacetime and Geometry by Carroll are good popular choices.
If you're just looking for discussions about the twin paradox here's a good answer on stackexchange: physics.stackexchange.com/a/242044 . I also enjoy this rant: rantonels.github.io/twin-paradox-for-literal-children/
@Paras Sharma The explanation of the twin paradox being caused by not traveling along the geodesic for a single twin is in the first chapter of "Spacetime and Geometry" by Sean Carroll
So are gonna have to wait another year for another video on this from you?
We understand your frustration, and apologize as this is a spare-time effort. Our next video is almost complete, watch for it soon!
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.
Can the apparent acceleration of an object without internal stress be explained without invoking a global (“fictitious”) force?
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.
If the twins have to have constant acceleration, it must factor into correction for gravity for the twin moving away from earth. If not, whatever acceleration the twin moving away has will change as he leaves the gravitational field which will make the entire thing pointless. The correction is a default for gravity so that acceleration is the same throughout for both parties.
@@Ntnt11
We are talking about SR. Gravitational fields are weak, their potential wells are shallow, so it's not about one twin leaving the gravitational field of her/ his home.
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.
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?
both twins agreeing on who is accelerating is what solves the paradox? If both have a pendulum, only the one is the ship will tilt as the ship accelerates, the one in the earth doesn't move; how do u explain this?
If you free fall through gravity, you are accelerating but can't measure it. You can only measure acceleration relative to a pendulum that isn't accelerating. Also the measurement itself is relative. It's equally valid to say the pendulum is accelerating and you aren't, or that the ground is accelerating towards you.
Not even an expert but its obvious that you mean choosing a pendulum relative to earth will tilt in the aircraft which by default means agreeing that earth will not be the one accelerating.
If you put a pendulum from the aircraft on earth, it will tilt on earth.
The creating of the video is arguing the exact thing you are saying. There is 0 reason to consider that earth is not the one accelerating. Pendulum will not tilt on earth if you choose a pendulum thats from earth. If you choose a pendulum from another reference frame, pendulum WILL tilt on earth.
@@Ntnt11 it seems u got the gist man; how is this problem solved?
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.”
This is so very wrong. I was subscribed but there are too many nonsense videos
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.
Hey John. Yes, the person in the rocket sees the stationary clock in motion. Your statement that "both observers can claim that the other clock is slow" goes to the heart of the twin paradox. What makes one twin's motion more real than the others? Time dilation is a real phenomenon (we see it frequently in experiments) but current theories are ambiguous when it comes to explaining what privileges one twin's time-dilation experience over the other's.
Dialect 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? Maybe this is the same question... but takes away the acceleration or turn around potentially differences or confusion points.
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.
And, there is even simple experimental proof, without a Paradox, on Earth: Put one clock on the Mt Everest, and one on sea level. After a decade, or so, the clock on the Mt Everest will have ticked "slower" by a fraction of a second, as it travelled a significantly longer distance through space, experiencing a higher acceleration from the Earth rotation.
If acceleration counts, shouldn't DEceleration also have effect?
exactly, it does...
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.
I was just about to say the same thing.
Great answer!
@@pawelwysocki1581 yeah it just naturally flows out of the mouth
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.
If you invoke a pseudo-gravitational field for the accelerating observer, then yes, that is a correct way to describe the conventional solution to the paradox (see our video Einstein, Gravity and the Twin Paradox). However, it still rests upon the assumption that one observer can be determined to be "absolutely" accelerating, even though that notion is poorly defined.
@@dialectphilosophy thanks for replying man, I've seen all your videos and have been thinking about this a lot. And I think we can objectively define who accelerates by looking at spacetime curvature and/or change in total energy.
The curvature of spacetime in a given section of the universe is objective and not relative, since it's a function of energy density. So in the case where neither twin expends nor experiences an energy change, the accelerating twin is the one that travels through the more curved region of spacetime.
Now in the scenario where they are both in regions of similar curvature, the accelerating twin is the one who expends energy or has energy added to him from external, ie. the one who's total energy changes. And this twin experiences dilation depending on the direction of motion, so slower if he moves into the curvature and faster if he is moved away from the curvature. We can sort of think of changing his energy as smoothening out the spacetime in his region, and so he ages faster.
Do let me know if I'm on to something here. Love your videos, get more consistent and you could blow up. I remember subscribing to Arvin Ash when he had fewer subscribers than you and he's big now, so you can too. Thanks.
@@caveman36 Thanks! We appreciate the encouragement, and plan to ramp up video production next year!(And expand to new topics as well) You’re correct again that under the theory of general relativity, curvature at any point is indeed objective. But in regions of flat or similar curvature, energy expenditure is again related to the notion of absolute motion and who is/isn’t accelerating. So there is still this issue, when we reduce the GR manifold to its smaller, stitched-together SR components, of what really determines the “absoluteness” of accelerative motion.
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.
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?
According to the perspective of starship, yes.
@@Andrew0you0tube
Don't deny that, but one perspective is wrong. The one doing the acceleration/turning on and off of the engine. And then claim those forces were acting on the earth instead of the space ship. One perspective is correct not both. A ball hanging from the ceiling will show those forces. The spaceship will see a ball hanging on the ceiling at rest on earth. It cannot see forces acting on the earth and still claim they are responsible for the acceleration of the earth towards the 🚀.
But if acceleration is not distinguishable, if there was some way to accelerate without subjecting occupants to inertial forces. Would the paradox even exist? Well, no. Because removing the inertial forces by necessity removes the temporal effects, the time gradient that would cause accelerometers to move. If neither twin experiences time differences, their times remain the same!
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.
There is "Twin paradox". Paradox it's something that we misunderstand due to fake assumptions and we are surprised by the outcome. But It may be truth. In case of TP its real effect but Is contradictory to intuition.
The paradox is about 2 people born the same day and time and they have different ages.
Our human intuition perceives is to be deeply wrong, while it's a true fact.
The paradox is NOT about whether twin A should be younger than twin B or viceversa.
Whether twin A is younger or twin B is younger is a paradox beside the main paradox.
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?
Can´t one use a Loedel diagram in the middle and conclude that they are both the same age when they meet again? All times and distances add up to the same value for both as it is symmetrical.
Please make another Video. I think your resining is festinating. I would love to hear your take on the solution of the paradox.
Einstein is wrong. That is the answer!
@@joeboxter3635 thats a little to easy.
Acceleration is absolute.
no
Once you start accelerating, you are not in inertial frame. Your description of surrounding isn't will not follow physics, youll have to use pseudo forces.
Assume yourself spinning like a ballet dancer, you feel the force on your arms pulling you out. Now remove everything you see, earth 🌎 ⛅ 🌒 and now you r in space. You cant see you are rotating, bt you still feel the acceleration on hands, they will be pulled outwards.
So acceleration is absolute.
While you press the gas pedal , others start accelerating but that is because you're frame isnt intertial, that 1st law of motion doesn't hold. And for fixing this you ll have to use a pseudo force.
@@ev2839 doubt it
Accelleration is absolutey relative to the plank length which is the same size everywhere. As a body accelerates it changes its scale relative to the plank length resulting in an associated force.
Or.. how I see it...
The smallest point location, the closest to nothing we can get is a point that collapses in on itself at the highest possible rate.. in same way that there is a max speed C there is a limit to the smallest size. The smallest point there is,is the very same point everywhere. Ie zoom into the smallest particle on the Moon down in to the centre of an electron for example.. and you would find the very same location if you zoomed into an electon inside a piece of matter on Earth. This btw is how entanglement works as at the smallest scales all loctions in the Universe.. distance infinitesimals points are all the one and the same location. As John Weeler said.. there is only one electron. It is this one point that gives an absolute to acceleration and all acceleration is relative to it.
@@ABHINAN160898 this is not right.
You invoked the universe to say you are spinning. If there is nothing else to relate to you cannot say you are spinning or doing anything else!
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!
I believe he made a mistake in 9:39 by setting t_B=t'_A=sqrt(3), instead of t_B=2.
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?
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".
Hey Mike, thanks for the comment. We do not claim that the situation between the twins is symmetrical, only that the breaking of the time-dilation symmetry is not due to acceleration. The idea of inertial forces as being responsible for breaking the symmetry was discussed briefly in our last video, Can You Feel Force, and will be addressed again when we release the follow-up to this video. As it turns out, the role of inertial forces is highly problematic due to ambiguities in the definition of "inertial".
If your argument is that they are not symmetrical, because the accelerated observer can feel a force. Then what if the accelerated observer is in a field causing acceleration towards the earth and accelerates all objects in the ship equally? Since everything in the ship would be interacting with the field equally that would mean all objects in the ship would be decelerating equally and there would be no way of detecting the acceleration. Its also the reason why we can conclude that gravity is not a force, its because a falling observer cannot do any test to conclude that they are accelerating.
The feeling a force argument also does not work if you consider acceleration on a particle. This is because there is no other particles to measure acceleration compared to each-other.
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.
You don’t understand acceleration. As a description of motion it’s only definable in a relative context. “Absolute acceleration” is entirely undefinable, and even Einstein thought it made no sense. What we attribute as absolute “physical acceleration” is only an empirical intuition derived from everyday experience, much like absolute space and time once were. It’s good to see people like Dialect finally calling these arbitrary prejudices into question.
Glad I stuck around till the end, really gave me a good idea on what the paradox actually entails and why the solution doesn't lie in the math. Really interesting.
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.
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
Clever, and It's not a heresy, but with a correction:
APPLYING RELATIVITY CARELESSLY IS WRONG!
I think you have just summarized the GTR, which applies to objects in the presence of gravity and/or accelerating. In both cases STR is not applicable what the other videos forget to mention. But in both, STR and GTR speed is defined as a relative property. There is no absolute speed, position and time.
The equations don’t mention relativity because the equations assume relativity. The equations are the emergent result of assuming Relativity. Relativity was a Greek principle that led to simple equations of motion. Many of newtons laws were emergent from Greek relativity. At the time the main thing they believed was relative was velocity. Einstein just figured out how to expand it in ways that resolved apparent contradictions in Newtonian physics and theories of electromagnetism. His equations are what emerge when you assume certain things such as light is constant speed for all observers and assume that external velocities AND distances and rates of time cannot be measured absolutely but can only be measured relative to different reference frames. Anyway, relativity is valid, if anything more valid than the equations themselves. (Oversimplifying here is killing me but it’ll have to do. Also I think this video is off-base on many points, acceleration is not relative in this context the way he is trying to say it is. There is a clear picture of who how each of their reference frames are changing and they are very asymmetric)
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?
Tell me this, if the twin B rotates around its own COG, you seem to claim that it would be indistinguishable from turning twin A around B's COG. But I thought you had to apply a torque to the mass to be able to rotate it. The math will not be the same if I'm turning my 1000kg around my own center, versus turning the entire rest of the universe around my center... What am I missing?
Finally someone could explain my concern about this paradox! Thank you!
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.
why not? Becuase he can measure the force?
@@klas7988 Yes, that is exactly the reason. he can measure the acceleration
@@riverchess-so7pr Correct. You can measure acceleration a hundred different ways.
But the acceleration can just as easily be measured as the pushing away of on object while you stand still as it can be interpreted as the pusher accelerating away from a still object. Just as my jumping off the earth one foot can be interpreted as me pushing the earth away from me one foot. There’s a perfect symmetry in measuring acceleration. Acceleration is necessarily relative. This is why it’s problematic to consider whether there’s an ether. If there’s an ether, then absolute acceleration would make sense relative the fixed ether. The ether is like God for Newton (who needed God to make sense of absolute time and absolute space in his arguments vs Leibniz).
But the twin paradox and relativity assume no ether. So with no ether, there can be no absolute acceleration. You also get perfect symmetry.
@@riverchess-so7pr Gravity is a form of acceleration, correct?
So is the apple falling towards the Earth or the Earth towards the apple? And why?
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.
RE: "Deep space" ... "Great attractor" ... "Other person" ...
The other person is equally as valid reference frame as the Earth, the Great Attractor, or my ass. The laws of motion do not require any special reference frame. *No reference frame is special* ! You do not need to be conscious to "experience" the difference between being in an inertial reference frame vs. being in an accelerating reference frame. You don't need to know about anything else in the universe to measure proper acceleration in your own local reference frame.
The CMB is exactly as arbitrary a choice of reference frame as using the Greenwich Observatory in London, or the planet Saturn. These are all equally valid.
@@juliavixen176 they are not equally valid. The observatory is on earth, which everything on earth is all travelling at the same speed in reference to other things also on earth. Saturn is not travelling at the same speed as earth.
The satellites in orbit also are not travelling at the same speed in reference to things on the surface which is why their clocks need to be synchronized regularly. This has been proven even with atomic clocks.
If you're struggling with this, I have an add-on video that may help: ua-cam.com/video/_3jwoQkgc5k/v-deo.html
Isn't this already solved by the calculation of GPS satellites and adjusting for the difference in time experienced there?
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.
Einstein himself and many others all agreed acceleration is relative - like space and time, it is a mathematical construct. Your confusion comes from coordinating something mathematical to something physical - “feeling force.” I’d check out his other videos on this topic, Newton vs. Mach is a good one, or “Why Relativity Doesn’t Add Up” talks about why Einstein believed acceleration was relative
Including acceleration in a gravitational field.
@@WSFeuer No, space and time are not mathematical constructs. Mathematical constructs-- models- are created to try to understand the underlying reality.
If we can't agree on that, I'm afraid were are not even speaking the same language.
There are senses of the word "relative" where acceleration can be called relative, but this just shows the difficulty of describing complex models like relativity (and actual reality) in language that wasn't created with scientific or mathematical precision.
Likewise, I'm not confusing reality with a model when I mention feeling a force. This is simply an attempt to illustrate that one situation is very different than the other. This "feeling" itself isn't force or acceleration or whatever.
@@WSFeuerThe fact that acceleration is absolute is one of the key importances of SR and GR. Acceleration is measurable and can be measured absolutely, just like rotation. You know why rotation can be measured absolutely? Because rotation is just constant acceleration.
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.
I think he believes that there is no way to tell who is accelerating relative to who but he’s wrong. Unlike constant velocity, acceleration is absolute. If Einstein is accelerating towards Emmy then he will certainly feel the force that is acting on him. When pressing the brakes of a car and it almost throws you out the window, an observer does not experience those effects relative to you. That is to say the effects of acceleration are local and absolute
"WHO is accelerating?". Well in Alice's reference frame, it is Bob who is accelerating. But in Bob's reference frame, it is Alice who is accelerating. Hence the paradox.
The solution, I believe, lies in asking who is accelerating according to an INERTIAL REFERENCE FRAME.
Acceleration IS relative, just like velocity is. However, what is absolute is your acceleration relative to an INERTIAL REFERENCE FRAME. @@orionkenya1 If you're accerating at 20m/s/s relative to one inertial reference frame then you are accelerating at 20m/s/s relative to ALL inertial reference frames.
@@Dekoherence-ii8pw Dialect seems to think that you can't establish the inertial frame of reference. At least that's what I've got from his video "Can you feel forece?". Total BS.
Dear Dialect, I would like to address your statement at 4:37 in one of your videos, where you claimed that the solution proposed by minutephysics is symmetric with the lines of simultaneity when the coordinate system is changed. However, I must respectfully disagree with your assertion.
To help clarify this concept, let us imagine a space station with two lights, A and B, representing events in spacetime. Suppose these lights flash simultaneously according to a Twin on Earth (for ease of understanding). However, when a rocket Twin starts moving away from Earth, they will observe the flashes of light occurring in a different order due to the relativity of simultaneity.
Both Twins can keep a record of the events they observe throughout the journey. In Earth's Twin reference frame, events AB occur simultaneously throughout the journey. However, in the rocket Twin's reference frame, the order of the events loops: B first then A during the outgoing journey, and A first then B during the incoming journey.
It's worth noting that if we choose a different reference frame, the order of events will be different. This demonstrates that lines of simultaneity are not symmetric, and different reference frames will not agree on the order of events. This phenomenon provides a resolution to the Twin Paradox.
You're assuming that we're not allowed to say that it is the space-station and earth which have switched reference frames; then the reversal of the order of events would be attributable to the acceleration of the space-station, not the rocket observer.
Not in SR tells us why we're not allowed to describe the earth or space-station as acceleration and switching frames, which is why drawing the symmetric lines of simultaneity diagram is indeed accurate.
@@dialectphilosophy Well, the Lorentz transformation cannot turn a zigzag line into a straight one. Even if you try to make the moving twin's world line straight, the transformation still cannot remove the zigzag from their world line, assuming they can accelerate instantaneously, leaving a zigzag. That zigzag proves that the moving twin occupied more than one frame.
In my example, I am assuming that the station was in an inertial reference frame all the time, and we can use the order of events from the station to determine who was changing frames.
@@Mysoi123 The Lorentz transformations only be applied between inertial frames (non-inertial frame transformations require covariant extension). Therefore, you have to have a mechanism to determine which frames are inertial before you are even allowed to use the Lorentz transformations. SR provides no such (unambiguous) mechanism.
Does an atomic clock kept in a higher altitude ticks diffrent from that of another atomic clock which is kept in a lower altitude? If the former ticks differently compared to the latter, does it prove time dilation? If time dilation is real, does it prove special relativity( special relativity involves motion , and the above two atomic clocks are static in two diffrent altitude)?
You presented valid proof backed with an experiment so he ignored you.
not just atomic clock but any clock will tick at a faster rate at higher altitude because higher altitude means lower gravitational field. But that is gravitational time dilation an effect coming from General relativity. Twin paradox is a narrative in Special relativity where time dilation is a consequence of invariance of spacetime interval between two events.
BTW, time dilation is experimentally verified many times, both gravitational and otherwise.
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.
the paradox is that you can’t decide which of the two objects is the one “actually” accelerating
@@pe1900 How about the one emitting reaction mass? Am I supposed to believe that an object can just change momentum spontaneously, without it being conserved in the form of exhaust?
@@WWLinkMasterX it's a thought experiment, that obvoiusly can't happen, we're theorizing about what would happen if it could
@@pe1900 Then you're entertaining physics that are verifiably false, and the whole premise is moot.
the watcher would feel the force
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.
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.
1)on 9:20, you say that ALbert would want to calculate what her coordinated read in his frame. Isnt that the same thing as you calculated a second earlier (x=c, t=2)???
2) it doesn't make sense to me me why the space coordinate of Albert should read zero in her frame, because he was travelling for 2 years at 0.5 c, so should have been at c distance. At this point, I also don't understand whether the x or x' in your calculation stands for distances travelled or coordinates, because you substituted x=c, which seems like x is the distance between them instead of 0 (if x means her own coordinate in her frame). If that substitution of x=c is correct, does x mean the coordinate of Albert as seen from her frame, and consequently x' the coordinate of Albert in his frame (which, in all cases shall be zero-and so this interpretation of mine must also be wrong else we substitute x'=0 everywhere)?
3) How to decide when to use inverse or direct transformations??
COuld you just make a video explaining the meaning of the Lorentz transformation equation symbols, and how to to use them for the scenario you showed?
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 UA-cam 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.
Tl;dr. It was acceleration all along. The best source on this subject on UA-cam is imo the Fermilab channel.
You are a very firm teacher; 😎
Acceleration is not relative.
What if Albert does his turn on a black hole without acceleration, since from his point of view he's going on the only possible path that is bent by black hole gravity
It is still an acceleration, he only uses a different motor. In Emmy's reference frame he is clearly changing his velocity (a direction of it, to be precise). The nice thing about using gravitational slingshot is that all object in the spaceship are pulled, not only the fuselage, so the passenger will not feel that acceleration.
IMHO gravity and acceleration are the words which are marking the point where STR does not apply any more.
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..
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.
Agreed. If science ultimately depends on what is actually observed in the "real world," consider an airliner plunging vertically into the surface of the earth at 600 mph. Now did the passengers stay stationary while the earth moving at 600 mph came to a sudden halt? Or was it the passengers who experienced an extreme change in velocity? Well, which are the ones who actually appear on TV afterward to tell about what happened?
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.
You can not solve it by drawing it correctly. Why?
You have to explain it correctly so you can draw it correctly. If you can not do that, what does that tell you?
Think about ir Rajesh.
But wait for iiitttt. If you explained it correctly, there will be no need for diagrams and formulas.
What are you feeling when you 'accelerate', then? Why do you feel it? How can it be that something measures change of a singular variable, which then changes based on perspective? How does that not suggest that said singular variable cannot be measured objectively, or that it is not being measured objectively? Is it not true that regardless of whether or not light has hit your eyes and you recognise an event as happening, there had to be some point in time in which it actually happened, perhaps predating the moment at which you realised it happened? Would you not be able to find this, except in specific situations, by using two observers to figure out the difference? What causes aging or lack of aging in this context? No explanation seems to make it any clearer. Perhaps, I am too stupid to understand it. Not sure.
Suppose there are two planets A and B very close to each other and suddenly we give a velocity to both of them in the opposite directions. Both of them have the same mass and opposite velocities suddenly. Now as they move apart, due to the gravitational attraction their speed will continually decrease, become zero then increase and then after some time they will appear to be moving towards each other. Both of them are accelerating at each and every point of time. Which of them will be older? When they are about to collide?
The conventional answer, taken from a frame of reference in which both their accelerations are considered to be "real" or "objective", is that the planets age the same. Each planet will observe time dilations due to the other's velocity, but these dilations will be balanced out once the planets start moving back towards each other due to the equal and opposite accelerations.
@@dialectphilosophy right
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.
The issue is, what is the mechanism for determining who accelerates vs. who doesn’t? SR does not suggest a clear methodology on this point, so both twins should have equal right to draw their own spacetime diagram. Check out our other videos for deeper analysis into why acceleration can’t just be “felt”!
@@dialectphilosophy Maybe SR doesn’t but in GR the equivalence principle states that there are locally inertial frames. The problem is that local means an infinitesimal neighborhood and any accelerometer would take up a finite amount of space. So inertial usually means Taylor expansion of the metric about a point agrees with the minkowski metric to second order. That being said, we have accelerometers that can measure space time gradients so if the gradient deviates beyond the second order approximation then we would say we aren’t in an inertial frame. A simple example would be using a device with 6 weight scales holding objects of the same mass oriented on the axes of your reference frame.
My response sounds pretentious so TLDR: you can have flat space time over a small distance and we can check if it’s flat using multiple accelerometers
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 applies on accelation too as inertial mass and gravitational mass are the same. Special relativity is only concerned with uniform translational movement, ie velocities. This is what causes the time dilation. The acceleration part is used to explain the "paradox" ie why it only happens to one twin.
The paradox can be resolved without acceleration or turning around as long as you give each an intiial starting co-ordinate and ending co-ordinate at constant velocities. When any journey is done neither can tell which is moving, however when the clocks are stopped only one has actually changed co-ordinates, ie gone somewhere, travelled a distance. This distance infers a velocity and therefore a time dilation as per the Lorentz transformations.
You can also think of it as a sea of clocks that all have a position during the experiment. None of these sea of clocks changes position either and niether of their clocks has any time dilation. These can be thought of as external observers.
NOTE
In real life, "twin" particles in experiments such as cosmic rays, particle colliders etc show differeing ages without any need to accelerate. Only one "twin" in the particle pairs shows time dilation, the one that is moving at constant velociy, there is no paradox. Same for GPS and other satellites that have to a correction factor for special relativity as well as general
@@zakelwe "special relativity is only concerned with uniform translational movement ie velocity". Its wrong. Special Relativity works fine with translational, rotational, acelaration, Sagnac Effect considered by GPS, etc. The Rindler coordinates is Special relativity and we have acelarations. But the Ricci curvature of Rindler space is zero, it's a flat spacetime. In any case we don't have curvature (but with acceleration) the special relativity work fine, uniform movements ou rotational platform like Sagnac Effect.
This clears up a huge amount of confusion
It would be interesting to add a third subject, who acts as an spectator that remains at the starting point since for him, both twins would've aged the same (I think, this may be dumb). It would also be interesting if the paradox happened in a "spherical" universe (I'm not sure how to put it) so that no acceleration is needed for them to meet again. What would happen then?
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.
How would you define "turning back?" Could you produce a definition that doesn't somehow invoke a measurement of relative acceleration to a fixed reference? (Hint: you can't. See our video "Do Inertial Frames Resolve the Twin Paradox" or "Newton vs. Mach" for more on this topic)
@@dialectphilosophy If you are in an inertial reference frame and do some experiments, you can determine the laws of physics. If you are in a reference frame and do some experiments, you can realize whether you are in inertial or non-inertial reference frame. If you are in non-inertial reference frame, the laws of physics is not valid. As you are inside a reference frame, you can easily determine whether you accelerate or not. You don't need to look outside from your reference perspective.
The word "turning back" is a daily word to simplify the understanding of the movements. From my perspective, "turning back" can be a word to explain one type of the acceleration. You can consider the word "turning back" which is a process at such a time interval when the laws of physics is not valid. Thus, in the "turning back" process, you won't measure a relative acceleration.
On the other hand, jumping from one inertial frame to the other is nonsense. There isn't any physical meaning of that. Even if there was a physical meaning, it wouldn't give the chance of a precise measurement. For example, you want to meause the length of a rod by using ruler. When measuring it, you don't change your ruler. If you change, how can you trust your measurement?
As I am a theoretical physicist, I want to say that twin paradox isn't a paradox. Sure, this doesn't make me right but I don't know your intention.Thus, I don't want to spend my time to explain myself.
@@dialectphilosophy I'm sorry, but you're just flat-out wrong. You can easily measure your proper acceleration (your acceleration measured in your momentary intertial coordinate system) for example by mounting a laser and a spectrometer on the opposite ends of a chamber carried on the ship and checking whether the laser blue- or redshifts along the way. The earthbound twin will measure her proper acceleration to be zero (ignoring the effects of Earth's gravity), while the traveling twin will measure it to be none-zero somewhere along the way. That is what breaks the symmetry.
Acceleration is not relative in special relativity, and in fact can't be since "special" specifically refers to the fact that it only applies to inertial (non-accelerated) reference frames, which would be a nonsensical restriction if you couldn't tell inertial and non-inertial frames apart - in other words, in SR physics behaves differently in inertial and accelerated frames. GR does away with this restriction by introducing a metric which tracks what "coordinate effects" (or "gravity") are present in each reference frame which, again, vary between the twins, again breaking the symmetry.
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.
inertial frames of reference can't "turn around" ... what if you are orbiting?
As far as I understand it, the Equivalence principle says nothing about acceleration being relative or not. All it says it that an accelerating frame and a gravitational frame are indistinguishable.
@@whuang23888 then you are in a rotating frame of reference and not in an inertial frame. Only a frame of reference in freefall in a homogeneous gravitational field is inertial. And that frame also cannot turn around.
@@afalco54 i believe orbiting objects due to gravity field is in freefall/inertial state, at least based on this author's videos ....
@@whuang23888 Free falling frames of reference are inertial only in a homogeneous gravitational field. Of course when you select a suitable small region of space in which the inhomogeneity of the gravitational field is not felt you may consider yourself being in an inertial frame. However even in this case when you are orbiting you change those localized inertial frames all the time, even if you don't experience the change.
i know it's complicated, but hey, nobody said physics is easy...
How can you draw the frame of reference of an objection ("Albert") that changes direction as a straight line? Straight line can only represent inertial frame of reference (zero net force acting on it, moves with a constant velocity). That's the key problem with the video, nothing else to say. Ironically, mistake in this video made me understand better the world line explanation from other videos.
One thing I agree on is that gravity explanations raise questions... I mean, if only the acceleration matters, doesn't matter if the twin travelled 50 years or 1 day.