AndreusMaximus
Master
So for anyone on here who is interested in Einstein's theory of relativity (like me) or knows much about it (unlike me) here's a little something I've been working on for a while. I posted this to a physics forum that I just signed up for today (INGO, I cheated on you with another social media platform; please forgive me!!!) hoping to get some feedback, but thought I'd also post it here, too. I purposefully avoided any math to try and keep the basic principles in the forefront, so hopefully anyone who has a basic grasp of what the theory of relativity is should be able to read an understand it.
So I've been trying really hard to understand the theory of relativity at its most basic level lately, and recently I dove down the rabbit hole of the Twin Paradox. This has led me through a series of youtube videos, each one claiming to present a different solution, explain why the other videos presenting other solutions are wrong, and finally ended me up on a video that claimed to poke holes in the logic used by all the other videos, leaving me very confused.
At first I felt like I really wasn't understanding any of it, but I think I was finally able to formulate an answer that makes sense. To help me with this, I made my own, simplified, version of the Twin Paradox below. If anyone would be willing to take the time to read 1) My simplified/slightly modified Twin Paradox, 2) My paraphrasing of the video I saw that claims the paradox is still unresolved, and 3) An explanation, in my own words, of what I understand to be the real resolution of the Twin Paradox, and then let me know if what I have said makes sense or if I'm still missing the whole point, I would be extremely grateful!
(Note: I shorten "inertial frame of reference" to "inertial frame" throughout this whole thing; hopefully that's not too inaccurate or confusing!)
1) My "Simplified" Twin Paradox
Consider a universe that behaves exactly like our own: all the laws of physics are the same, the theory of relativity applies, etc.
This universe contains nothing whatsoever except two spaceships, each of which has one observer and one clock in it. The observers are named Bob and Rob. At the start of our thought experiment, the two spaceships are sitting next to each other, motionless relative to each other. (Gravity in this thought experiment is considered negligible, and thus ignored.)
An event occurs in which the two spaceships move apart from each other, then come back together.
From observer Bob's perspective, it appears that Rob's spaceship accelerates rapidly away from him, quickly reaching a speed very close to the speed of light, then, when Rob's spaceship is several light years away, it suddenly appears to accelerate rapidly in the other direction, and begin to travel back towards Bob, again quickly approaching the speed of light, then finally when it is close to Bob, Rob's spaceship appears to decelerate extremely rapidly, and comes to rest next to Bob's spaceship, leaving the two spaceships motionless relative to each other, in the exact same position as they were at the start of our thought experiment (again all of this from Bob's perspective.)
What does Rob see from his perspective? Well, just copy and paste the above, switch Bob and Rob's names, and the event will look exactly the same to Rob, only mirrored.
Finally, ask the question; for whom was time experienced more quickly relative to the other? Did Bob experience a longer time and Rob a shorter one, or vice versa?
2) The Claim That the Paradox is Unresolved
Now, the consensus of all the videos I've seen on the Twin Paradox seems to be that the Twin who remains still will age more quickly than the one who moves.
HOWEVER, the whole point of the relativity of motion, is just that; motion is relative. In the above example, Rob observes Bob move away from him, then back to him, himself remaining still. But observer Bob sees himself as remaining still, while Rob moves away, then back to him. According to relativity, neither Bob nor Rob is more correct or incorrect in their perception; both are correct given themself as the observer.
So how do you know which one experienced time more quickly? Taking planets and other things that we perceive as stationary out of the equation, Bob and Rob have no way of knowing which one of them actually moved, and which one didn't, therefor, there cannot be any logical way of claiming that one would have experienced time any differently than the other.
3) My Paraphrasing of the Real Explanation (or what I hope is...)
It seems to me that much of the confusion surrounding what is the correct solution to the paradox stems from conflating acceleration with changing one's inertial frame. It appears to me that acceleration simply meaning changing one's speed relative to an observer. If this is the correct definition of acceleration, than a person in free fall will be accelerating relative to an observer on the ground. However, they will NOT be changing their inertial frame; to an observer on the ground they will be in motion, but in their own space-time a person in free fall is not moving or accelerating at all; they are simply remaining in the same space as that space curves towards the mass that is bending space (I'm sure there's some inaccuracies in how I described that, but that's the best I can put it.)
Thus we can see that acceleration and changing one's inertial frame are not the same thing. You can accelerate without changing your inertial frame, like the person who is in free fall does. You can also change your inertial frame without accelerating relative to a given observer, like two people who are in cars that go from 0-60 in the same direction at the same time: relative to each other they haven't accelerated or even moved, but they've both definitely changed their inertial frame. Acceleration is something relative to an observer; it can change based on which observer you're looking from. Changing one's inertial frame is something objective, and is not at all connected to acceleration, other than the fact that in the physical world we often see objects that are experiencing a force that changes their inertial frame also accelerate relative to us at the same time, so we tend to confuse the two.
In the final video I watched, I think the guy was basically stuck on the question: "In a universe devoid of all other objects (ie, empty space,) how do you objectively tell if an observer is changing their inertial frame or not?" Since he conflated changing one's inertial frame with changing one's acceleration, he then argued that since acceleration is relative, and both twins can claim that they experienced no acceleration (from their own perspective as an observer) that it followed they can both claim to have not changed their inertial frame. But this is where he's wrong; acceleration, that is, changing one's speed, is relative to an observer. But changing one's inertial frame is an objective thing, and not relative to any observer. Anything that is changing its own inertial frame will appear to be changing its inertial frame to ALL observers.
So if changing one's inertial frame doesn't mean accelerating, what does it mean? My layperson's explanation of changing one's inertial frame would go like this: "Any time an observer is experiencing a force that their body's mass resists, they are changing their inertial frame." That's probably not a very precise way of putting it, but what I'm basically trying to say is that if there is a force that cause an observer to change the way it would travel through space-time if that force hadn't existed, than the inertial frame of that observer has changed.
(Side note: In a way, I think it would be accurate to say that those who say the Twin Paradox is resolved because one twin experienced acceleration and one did not are partially right (or at least they have the spirit of the correct answer, and are just putting it wrong.) What they really ought to say is that since the "travelling twin" experienced a force that changed his inertial frame (which is the very thing that made him accelerate/decelerate from the perspective of the "earth twin") THAT is what makes the travelling twin experience time differently than the earth twin, and what makes their situation asymmetrical.)
So the final answer to my above modified "Twin Paradox" thought experiment is this: In order for Bob and Rob to have moved relative to each other, one (or both) of them had to change their inertial frame. If Bob changed his inertial frame, resulting in the relative motion, while Rob remained in the same inertial frame, then Bob will experience a shorter time during the relative motion, while Rob will experience a longer time. But if Rob changed his inertial frame while Bob did not, then when they come back together it will be Rob who experienced less time passing. During the motion, the one who is experiencing the change in inertial frame will experience evidence of this because the mass of his body will resist the change, meaning that he experience something that feels like gravity (even though, of course, it has nothing to do with gravity) pulling him towards the side of his spaceship opposite of the direction he is moving in. The one who is not changing his frame of reference will not experience this. Of course, a third possibility exists in all this, which is that the relative motion that Bob and Rob perceived was caused by both of them changing their inertial frame. For instance, they could have both had a change in their inertial frame that was equal but opposite, and thus, to an observer who started out at the same location as them but didn't change their inertial frame, Bob and Rob would have appeared to move in opposite directions at the same speed, and for the same time and distance, and then started moving back towards each other and come back to rest at the same starting point as this third observer. If this is what happened, then Bob and Rob would both have experienced the same length of time at the end of the motion. In short, you can't answer the question "which of them, if any, experienced more time than the other?" without first knowing who changed their inertial frame in order to cause the relative motion in the first place.
(Other side note: There's also a really funny aspect to this thought experiment, which is this: Pretend that Bob and Rob are creatures who cannot feel the effects of the forces that change their inertial frame, and they and their clocks are both strapped down so they won't slide around as the inertial frame changes. Also pretend that the windows to their spaceships are one-way mirrors, so they can both look out and see the other spaceship moving off into the distance (they have really good eyesight and can see lightyears away.) But they can't see inside the other person's spaceship, and thus have no clue how the other person is experiencing time relative to themselves. If this is the case, then during the time that they are moving apart then back together, they will have no way of knowing which one is changing their inertial frame, and which one isn't, thus, at whatever point in time the two spaceships come back together, one of them will have just experienced a longer span of time than the other one, but neither one will know if they are the one who experienced the shorter or longer time, unless they are able to dock their ships together so they can go in and look at each other's clocks.)
So, if you read through the whole thing, thank you so very much! Please try to poke any holes in it that you can; I'm really trying to understand the basic concepts at play hear, and I'd love to be educated in how I can improve my understanding.
Some of the videos I watched, in case anyone is wondering:
So I've been trying really hard to understand the theory of relativity at its most basic level lately, and recently I dove down the rabbit hole of the Twin Paradox. This has led me through a series of youtube videos, each one claiming to present a different solution, explain why the other videos presenting other solutions are wrong, and finally ended me up on a video that claimed to poke holes in the logic used by all the other videos, leaving me very confused.
At first I felt like I really wasn't understanding any of it, but I think I was finally able to formulate an answer that makes sense. To help me with this, I made my own, simplified, version of the Twin Paradox below. If anyone would be willing to take the time to read 1) My simplified/slightly modified Twin Paradox, 2) My paraphrasing of the video I saw that claims the paradox is still unresolved, and 3) An explanation, in my own words, of what I understand to be the real resolution of the Twin Paradox, and then let me know if what I have said makes sense or if I'm still missing the whole point, I would be extremely grateful!
(Note: I shorten "inertial frame of reference" to "inertial frame" throughout this whole thing; hopefully that's not too inaccurate or confusing!)
1) My "Simplified" Twin Paradox
Consider a universe that behaves exactly like our own: all the laws of physics are the same, the theory of relativity applies, etc.
This universe contains nothing whatsoever except two spaceships, each of which has one observer and one clock in it. The observers are named Bob and Rob. At the start of our thought experiment, the two spaceships are sitting next to each other, motionless relative to each other. (Gravity in this thought experiment is considered negligible, and thus ignored.)
An event occurs in which the two spaceships move apart from each other, then come back together.
From observer Bob's perspective, it appears that Rob's spaceship accelerates rapidly away from him, quickly reaching a speed very close to the speed of light, then, when Rob's spaceship is several light years away, it suddenly appears to accelerate rapidly in the other direction, and begin to travel back towards Bob, again quickly approaching the speed of light, then finally when it is close to Bob, Rob's spaceship appears to decelerate extremely rapidly, and comes to rest next to Bob's spaceship, leaving the two spaceships motionless relative to each other, in the exact same position as they were at the start of our thought experiment (again all of this from Bob's perspective.)
What does Rob see from his perspective? Well, just copy and paste the above, switch Bob and Rob's names, and the event will look exactly the same to Rob, only mirrored.
Finally, ask the question; for whom was time experienced more quickly relative to the other? Did Bob experience a longer time and Rob a shorter one, or vice versa?
2) The Claim That the Paradox is Unresolved
Now, the consensus of all the videos I've seen on the Twin Paradox seems to be that the Twin who remains still will age more quickly than the one who moves.
HOWEVER, the whole point of the relativity of motion, is just that; motion is relative. In the above example, Rob observes Bob move away from him, then back to him, himself remaining still. But observer Bob sees himself as remaining still, while Rob moves away, then back to him. According to relativity, neither Bob nor Rob is more correct or incorrect in their perception; both are correct given themself as the observer.
So how do you know which one experienced time more quickly? Taking planets and other things that we perceive as stationary out of the equation, Bob and Rob have no way of knowing which one of them actually moved, and which one didn't, therefor, there cannot be any logical way of claiming that one would have experienced time any differently than the other.
3) My Paraphrasing of the Real Explanation (or what I hope is...)
It seems to me that much of the confusion surrounding what is the correct solution to the paradox stems from conflating acceleration with changing one's inertial frame. It appears to me that acceleration simply meaning changing one's speed relative to an observer. If this is the correct definition of acceleration, than a person in free fall will be accelerating relative to an observer on the ground. However, they will NOT be changing their inertial frame; to an observer on the ground they will be in motion, but in their own space-time a person in free fall is not moving or accelerating at all; they are simply remaining in the same space as that space curves towards the mass that is bending space (I'm sure there's some inaccuracies in how I described that, but that's the best I can put it.)
Thus we can see that acceleration and changing one's inertial frame are not the same thing. You can accelerate without changing your inertial frame, like the person who is in free fall does. You can also change your inertial frame without accelerating relative to a given observer, like two people who are in cars that go from 0-60 in the same direction at the same time: relative to each other they haven't accelerated or even moved, but they've both definitely changed their inertial frame. Acceleration is something relative to an observer; it can change based on which observer you're looking from. Changing one's inertial frame is something objective, and is not at all connected to acceleration, other than the fact that in the physical world we often see objects that are experiencing a force that changes their inertial frame also accelerate relative to us at the same time, so we tend to confuse the two.
In the final video I watched, I think the guy was basically stuck on the question: "In a universe devoid of all other objects (ie, empty space,) how do you objectively tell if an observer is changing their inertial frame or not?" Since he conflated changing one's inertial frame with changing one's acceleration, he then argued that since acceleration is relative, and both twins can claim that they experienced no acceleration (from their own perspective as an observer) that it followed they can both claim to have not changed their inertial frame. But this is where he's wrong; acceleration, that is, changing one's speed, is relative to an observer. But changing one's inertial frame is an objective thing, and not relative to any observer. Anything that is changing its own inertial frame will appear to be changing its inertial frame to ALL observers.
So if changing one's inertial frame doesn't mean accelerating, what does it mean? My layperson's explanation of changing one's inertial frame would go like this: "Any time an observer is experiencing a force that their body's mass resists, they are changing their inertial frame." That's probably not a very precise way of putting it, but what I'm basically trying to say is that if there is a force that cause an observer to change the way it would travel through space-time if that force hadn't existed, than the inertial frame of that observer has changed.
(Side note: In a way, I think it would be accurate to say that those who say the Twin Paradox is resolved because one twin experienced acceleration and one did not are partially right (or at least they have the spirit of the correct answer, and are just putting it wrong.) What they really ought to say is that since the "travelling twin" experienced a force that changed his inertial frame (which is the very thing that made him accelerate/decelerate from the perspective of the "earth twin") THAT is what makes the travelling twin experience time differently than the earth twin, and what makes their situation asymmetrical.)
So the final answer to my above modified "Twin Paradox" thought experiment is this: In order for Bob and Rob to have moved relative to each other, one (or both) of them had to change their inertial frame. If Bob changed his inertial frame, resulting in the relative motion, while Rob remained in the same inertial frame, then Bob will experience a shorter time during the relative motion, while Rob will experience a longer time. But if Rob changed his inertial frame while Bob did not, then when they come back together it will be Rob who experienced less time passing. During the motion, the one who is experiencing the change in inertial frame will experience evidence of this because the mass of his body will resist the change, meaning that he experience something that feels like gravity (even though, of course, it has nothing to do with gravity) pulling him towards the side of his spaceship opposite of the direction he is moving in. The one who is not changing his frame of reference will not experience this. Of course, a third possibility exists in all this, which is that the relative motion that Bob and Rob perceived was caused by both of them changing their inertial frame. For instance, they could have both had a change in their inertial frame that was equal but opposite, and thus, to an observer who started out at the same location as them but didn't change their inertial frame, Bob and Rob would have appeared to move in opposite directions at the same speed, and for the same time and distance, and then started moving back towards each other and come back to rest at the same starting point as this third observer. If this is what happened, then Bob and Rob would both have experienced the same length of time at the end of the motion. In short, you can't answer the question "which of them, if any, experienced more time than the other?" without first knowing who changed their inertial frame in order to cause the relative motion in the first place.
(Other side note: There's also a really funny aspect to this thought experiment, which is this: Pretend that Bob and Rob are creatures who cannot feel the effects of the forces that change their inertial frame, and they and their clocks are both strapped down so they won't slide around as the inertial frame changes. Also pretend that the windows to their spaceships are one-way mirrors, so they can both look out and see the other spaceship moving off into the distance (they have really good eyesight and can see lightyears away.) But they can't see inside the other person's spaceship, and thus have no clue how the other person is experiencing time relative to themselves. If this is the case, then during the time that they are moving apart then back together, they will have no way of knowing which one is changing their inertial frame, and which one isn't, thus, at whatever point in time the two spaceships come back together, one of them will have just experienced a longer span of time than the other one, but neither one will know if they are the one who experienced the shorter or longer time, unless they are able to dock their ships together so they can go in and look at each other's clocks.)
So, if you read through the whole thing, thank you so very much! Please try to poke any holes in it that you can; I'm really trying to understand the basic concepts at play hear, and I'd love to be educated in how I can improve my understanding.
Some of the videos I watched, in case anyone is wondering:
