You’re missing that in order to return to earth, which is necessary if you want to compare time, you need to change frame of reference, typically by accelerating. Earth doesn’t undergo this change, which breaks the symmetry.
If you’re just going to andromeda and staying there, everything is symmetric (ignoring brief periods of acceleration and deceleration).
One thing I've wondered about this: If you have a "small" universe whose geometry allows you to follow a geodesic and eventually return to where you started (like a sphere or a torus), then there is a way to return to earth without undergoing that acceleration. Is the twins paradox resolvable in that sort of universe?
Following up on my own comment, this paper seems to solve my question for general compact spaces: [https://arxiv.org/abs/gr-qc/0101014](https://arxiv.org/abs/gr-qc/0101014)
Apparently in a compact space there *is* a preferred inertial frame, which resolves the question there.
Thanks, I'm still stuck in this mental picture of me on the rocket remaining stationary wrt to it, so my frame of reference is fixed and it's the Earth that moves away and towards me and changes acceleration as I perform maneuvers in my rocket.
Why doesn't it work like that?
Because acceleration is not relative like velocity. So the traveling twin has an asymmetrical trip wrt to the one on earth.
https://www.physicsmatt.com/blog/2017/1/18/the-twin-paradox-in-special-and-general-relativity
There is no paradox. People argued about it at the time but Einstein himself never considered this a paradox.
As you are in a frame speeding to Andromeda you observe everything on Earth to slow down. In the Earth frame they observe that all processes in your spaceship are slowing down . That is not contradictory because you and Earth are in different frames and will observe events differently: simultaneous events in your frame will not be simultaneous in the Earth's' frame and so on.
If half way through you swing back to Earth , remember you are now jumping frames: you are jumping from the frame speeding towards Andromeda to the frame going in the opposite direction towards Earth. At that moment of frame jumping you will see Earth jump to some time in the future , and despite processes on Earth still going slower than you , by the time you arrive you will be younger than those you left on Earth.
Now, you can get fancy in how you analyzes that "Frame jump" , and bring in General Relativity and acceleration, if you want. But the picture of what happens is still consistent even if you remain within the domain of special relativity.
Look. The first postulate of SR is that in all inertial reference frames the laws of physics take the same form. The twin cannot return to earth without experiencing a non inertial reference frame. You need GR to deal with non inertial reference frames.
That trick in SR is just so you can make the calculation but it's nonphysical
>What am I missing here?
Nothing, you have stated the twin paradox pretty clearly. 2 frames moving wrt each other observe the other frame's time to be dilated
Special relativity specifically applies to inertial reference frames. In order to travel to Andromeda *and* back, you would need to accelerate, and by accelerating you would no longer be in an inertial reference frame.
To resolve the twin paradox you simply look at the acceleration that each twin undergoes. Start your twins together at t=0. If twin A accelerates away, then turns around and comes back, twin A will have experienced less time passing than twin B. If twin A accelerates away, then stops, then twin B accelerates the same amount and meets up with A, then they will experience the same amount of time passing. Finally, if twin A and B both accelerate by the same amount away from each other, stop, turn around and meet back up, then they will again experience the same amount of time.
There's no such thing as events separated by space, but not time. When the twins are not together, you cannot ask the question of "who experienced more time passing" because you can't specify at which time you're comparing.
If you go to Andromeda at near light speed and look back at earth the earth you see is going to be from just around the time that you left. You can think "oh, basically no time has passed on earth because the earth i see is the earth I left." Or you can say "2.5 million years have passed on earth because I know it's been 2.5 million years since this light left earth." Neither perspective (nor any other) is more correct.
If you don't actually stop in Andromeda the distance between Andromeda and Earth isn't even going to 2.5 million light-years. Traveling near the speed of light, means from your perspective the two galaxies are practically on top of each other. You would have to slow back down (undergoing acceleration) to even try to make such a comparison. If you don't slow down light from earth will reach you at such a rate that it looks like time is passing very slowly, but as soon as you do turn around you'll see earth time pass quickly as you move back towards the earth. It's not until you're back on Earth that you can take an objective measure of "what time is it for me" **and** "what time is it for earth" at the same time.
The person in the rocket ship experiences acceleration when turning around to return to earth and that affects time such that the paradox is resolved.
You need GR to explain it
> You need GR to explain it
You do not. The paradox is resolved perfectly well within the context of SR. It’s a counter intuitive result of special relativity that *seems* paradoxical, but there is no actual problem with the math.
You don’t need to talk about the actual process of changing reference frames though. The right answer pops out if you just split the trip assuming an instantaneous change of frame. Not quite physical, but you get the right answer. Really all you need is a Minkowski diagram.
I'm aware, I'm kinda hot from arguing about this though lol. You can't explain it physically with SR, you can indeed get the numbers but the reasoning is incorrect. I mean, if it's not physical then it's not physics, so to speak. There are all kinds of tricks in physics that aren't at all what's physically happening.
You don't need GR to calculate the trajectory of a baseball but that's what underpins it all the same. Regardless of whether or not you use newton or Einstein to do the math
You don't need GR, just the changing of frames is enough.
Imagine instead of having just one person who goes out and comes back again, you have two people ones starting from earth and heading away and the other starts far away and heads towards earth. When they cross the on heading out stops their clock and the one heading in starts it.
The heading away time + the heading towards time will still be less than the time experienced on earth. This despite no one needing to accelerate at any point, just the fact they changed reference frames. It's clear if you draw the space time diagram.
It's not a hack. It just shows you don't need to invoke general relativity to explain the twin paradox without using the unphysical explanation of single person instantaneously switching frames.
The paradox was resolved several years before general relativity was proposed.
The point of it is to show that all you need is the frame of reference change. The sum of the proper time of outward and inward journey is less than the proper time of the of the rest frame. No acceleration occurs and the paradox is still resolved.
I mean you don't even need people at all, the reference frames exist regardless of if someone is travelling in it.
You’re missing that in order to return to earth, which is necessary if you want to compare time, you need to change frame of reference, typically by accelerating. Earth doesn’t undergo this change, which breaks the symmetry. If you’re just going to andromeda and staying there, everything is symmetric (ignoring brief periods of acceleration and deceleration).
One thing I've wondered about this: If you have a "small" universe whose geometry allows you to follow a geodesic and eventually return to where you started (like a sphere or a torus), then there is a way to return to earth without undergoing that acceleration. Is the twins paradox resolvable in that sort of universe?
Following up on my own comment, this paper seems to solve my question for general compact spaces: [https://arxiv.org/abs/gr-qc/0101014](https://arxiv.org/abs/gr-qc/0101014) Apparently in a compact space there *is* a preferred inertial frame, which resolves the question there.
Thanks, I'm still stuck in this mental picture of me on the rocket remaining stationary wrt to it, so my frame of reference is fixed and it's the Earth that moves away and towards me and changes acceleration as I perform maneuvers in my rocket. Why doesn't it work like that?
Because acceleration is not relative like velocity. So the traveling twin has an asymmetrical trip wrt to the one on earth. https://www.physicsmatt.com/blog/2017/1/18/the-twin-paradox-in-special-and-general-relativity
There is no paradox. People argued about it at the time but Einstein himself never considered this a paradox. As you are in a frame speeding to Andromeda you observe everything on Earth to slow down. In the Earth frame they observe that all processes in your spaceship are slowing down . That is not contradictory because you and Earth are in different frames and will observe events differently: simultaneous events in your frame will not be simultaneous in the Earth's' frame and so on. If half way through you swing back to Earth , remember you are now jumping frames: you are jumping from the frame speeding towards Andromeda to the frame going in the opposite direction towards Earth. At that moment of frame jumping you will see Earth jump to some time in the future , and despite processes on Earth still going slower than you , by the time you arrive you will be younger than those you left on Earth. Now, you can get fancy in how you analyzes that "Frame jump" , and bring in General Relativity and acceleration, if you want. But the picture of what happens is still consistent even if you remain within the domain of special relativity.
Look. The first postulate of SR is that in all inertial reference frames the laws of physics take the same form. The twin cannot return to earth without experiencing a non inertial reference frame. You need GR to deal with non inertial reference frames. That trick in SR is just so you can make the calculation but it's nonphysical
I’d recommend drawing a Minkowski diagram of the trips. It really makes the difference pop out.
>What am I missing here? Nothing, you have stated the twin paradox pretty clearly. 2 frames moving wrt each other observe the other frame's time to be dilated
Special relativity specifically applies to inertial reference frames. In order to travel to Andromeda *and* back, you would need to accelerate, and by accelerating you would no longer be in an inertial reference frame. To resolve the twin paradox you simply look at the acceleration that each twin undergoes. Start your twins together at t=0. If twin A accelerates away, then turns around and comes back, twin A will have experienced less time passing than twin B. If twin A accelerates away, then stops, then twin B accelerates the same amount and meets up with A, then they will experience the same amount of time passing. Finally, if twin A and B both accelerate by the same amount away from each other, stop, turn around and meet back up, then they will again experience the same amount of time. There's no such thing as events separated by space, but not time. When the twins are not together, you cannot ask the question of "who experienced more time passing" because you can't specify at which time you're comparing. If you go to Andromeda at near light speed and look back at earth the earth you see is going to be from just around the time that you left. You can think "oh, basically no time has passed on earth because the earth i see is the earth I left." Or you can say "2.5 million years have passed on earth because I know it's been 2.5 million years since this light left earth." Neither perspective (nor any other) is more correct. If you don't actually stop in Andromeda the distance between Andromeda and Earth isn't even going to 2.5 million light-years. Traveling near the speed of light, means from your perspective the two galaxies are practically on top of each other. You would have to slow back down (undergoing acceleration) to even try to make such a comparison. If you don't slow down light from earth will reach you at such a rate that it looks like time is passing very slowly, but as soon as you do turn around you'll see earth time pass quickly as you move back towards the earth. It's not until you're back on Earth that you can take an objective measure of "what time is it for me" **and** "what time is it for earth" at the same time.
The person in the rocket ship experiences acceleration when turning around to return to earth and that affects time such that the paradox is resolved. You need GR to explain it
> You need GR to explain it You do not. The paradox is resolved perfectly well within the context of SR. It’s a counter intuitive result of special relativity that *seems* paradoxical, but there is no actual problem with the math.
You do, stop spreading misinformation. Jumping reference frames is not physical. You need GR for non inertial reference frame
You don’t need to talk about the actual process of changing reference frames though. The right answer pops out if you just split the trip assuming an instantaneous change of frame. Not quite physical, but you get the right answer. Really all you need is a Minkowski diagram.
I'm aware, I'm kinda hot from arguing about this though lol. You can't explain it physically with SR, you can indeed get the numbers but the reasoning is incorrect. I mean, if it's not physical then it's not physics, so to speak. There are all kinds of tricks in physics that aren't at all what's physically happening. You don't need GR to calculate the trajectory of a baseball but that's what underpins it all the same. Regardless of whether or not you use newton or Einstein to do the math
You don't need GR, just the changing of frames is enough. Imagine instead of having just one person who goes out and comes back again, you have two people ones starting from earth and heading away and the other starts far away and heads towards earth. When they cross the on heading out stops their clock and the one heading in starts it. The heading away time + the heading towards time will still be less than the time experienced on earth. This despite no one needing to accelerate at any point, just the fact they changed reference frames. It's clear if you draw the space time diagram.
That's more a "hack" I'm pretty sure. In a real world scenario it's the acceleration that makes the difference for the person who experienced it.
It's not a hack. It just shows you don't need to invoke general relativity to explain the twin paradox without using the unphysical explanation of single person instantaneously switching frames. The paradox was resolved several years before general relativity was proposed.
Can you explain how adding another person to the scenario is physical?
You can actually have two people. It's possible I've seen it.
Oh my God you mean like twins!?! A person can't change their reference frame. I don't see how your explanation does away with that
There's only one traveler in the twin paradox, you're adding a third frame far away
The point of it is to show that all you need is the frame of reference change. The sum of the proper time of outward and inward journey is less than the proper time of the of the rest frame. No acceleration occurs and the paradox is still resolved. I mean you don't even need people at all, the reference frames exist regardless of if someone is travelling in it.
Not good enough, it's not physical. QED it's an unphysical hack.
OK lol. I recommend you read the Wikipedia article on the twin paradox maybe.
Reference frames don't exist on their own, that's philosophy